These "North Saxons" were exactly there where you would expect them, in the North of England — or were they? In any case, naming a region with a string of letters that somehow stuck was anything between 'just not important' to 'not really fitting anyways'.
For some breadcrumbs:
Annals of Ulster (Vol. I, ed. W. M. Hennessy, 1887), sub anno 912 alias 913: “ … Etulb King of the North Saxons died.” The “alias” dates in this section of the Annals of Ulster may be tested at several points and shown to be trustworthy. Ethelweard (Monumenta Historica Britannica, 1848, p. 520) uses a complicated system for indicating chronological sequence, but he clearly places the death of Eadulf (Athulf) in 913.
This is only a footnote for:
Approximate dates can be fixed to these events. Ealdred’s father, Eadulf of Bamburgh, died in 913. The first battle, the land-division and the punishment of the sacrilegious Scandinavian warrior all fell within Cutheard’s episcopate which cannot be extended beyond 915. Therefore the first Battle of Corbridge was fought between 913 and 915, and we should not be far from the mark if we put it in 914.
— F. T. Wainwright: "Battles at Corbridge", Historical Review, 1952. (PDF) [Links to WP added LLC]
Also compare The Annals of Clonmacnoise, being annals of Ireland from the earliest period to A.D. 1408.
In northern Mercia and Northumbria we see some 'Saxons' that are in the North and called by that name, 'Saxons of the North'.
The history of Northumbria in the ninth and tenth centuries is poorly recorded, but we do know that the Anglo-Saxon Northumbrian elite that held on in Bamburgh called themselves either ‘Kings of the North Saxons’ or Earls of Bamburgh.
— Dan Jackson: "The Northumbrians. North-East England and Its People. A New History", Hurst & Company: London, 2019. (p11)
But is that really so easy? Of course not.
(Also, keep in mind the date of the above passage.)
For illustration, from Wikipedia two maps, both not overly reliable and outdated (Britain peoples circa 600, Heptarchy):
The root cause for the legitimate curiosity displayed in this question is based on an anachronistic back projection of way more modern, or lets say younger concepts and meanings for words. These will cloud any proper understanding of the matter as it would have displayed itself in post-Roman and pre-Norman times.
And that is our way too stringent application of 'tribes', 'kinship' and consequently 'names' and gens/genetics concepts to a convoluted period of migrations, settlements and even conquests. In short: with all this heavy intermixing "there were not really 'Saxons' at all" might be a better description for a mixture of multitudes than "then the Saxons came and settled here".
This is very gradual process – that appears in written sources as a rapid and radical change – is visible for example in Germanic vs Britonic cemeteries, as for example in the region ending on -sex 'best documented', Wessex:
Distribution of Germanic burial sites in Wessex [after S. Chadwick Hawkes, The south-east after the Romans: Saxon settlement', in The Saxon Shore, ed. V. Maxfield (1989), fig. 27 and B. Cunliffe, Wessex to AD 1000 (1987), fig. 8.1]
— Barbara Yorke: "Wessex in the Early Middle Ages", Studies in the Early History of Britain, Leicester University Press: London, New York, 1995, p13.
Here we see that the 'origin' of Wessex population was a thoroughly intermixed settlement with a slight geographical and temporal gradient that peters out towards emergence of a new and more unified ethnos. But while the political power expanded from the 'tribe' called Gewisse located around the upper Thames valley, the earliest – yet for outr purposes quite late – Anglo-Saxon Wessex kings still bear Celtic names like Cerdic and Cædwalla…
This period of migrations and ultimately ethnogenesis is way less clean than necessary for such a simplifying description. While we like a stringent development with a nicely visible line going way back, what we do see is anything but. It is a grave mistake to think of 'Wessex as the land of the West-Saxons, where they came, conquered and then lived'. The geographical description is of later administrative origin. The name of a region itself and its etymology are far less revealing than some would like to think.
It is not a back-projection from the romanticising 19th century, that was delighted to find homogenous settlements of clearly defined groups, peoples and resulting kingships. Even the earliest and non-contemporary sources we have re-construct the past based on folk-etymology reasoning, blending out the not so simple process that lead to a 'found situation'.
The philologists themselves, of course, started from the universal assumption that language and descent went together, so that when they divided languages into Germanic, Latin, Celtic, and so forth, they thought that they were also dividing mankind into "races" of common descent and common inherited characteristics. The advance of genetics, linguistics, history, and archaeology ought to have revealed the fallacy in this, but unexplored assumptions are slow to change, especially if it suits politicians to use them for good or ill, to cement the political unity of those they rule or to divert collective energies into hating those who are labeled "outsiders." […]
From Italy come also references to the gens Anglorum et Saxonum, in which the singular gens preserves the compound implications that the et would otherwise deny. Meanwhile, the inhabitants of what would come to be called England were, by the early eighth century if not before, using the simple word “ English” (Angli, Anglici) to refer to themselves. As far as they were concerned, the name “Saxon” seems to have been reserved for the people of the southern kingdoms, while even southerners sometimes applied the description “English” to themselves as individuals and acquiesced in being subsumed under it as a group. […]
Against this background, our use of the word raises a lot of questions. When others called them Saxons and they called themselves English, did the inhabitants of England think of themselves as one people rather than as the sort of hyphenated compound—hyphenated but nonetheless distinct from all others—that might be inferred from our name for them? When did they become distinct from others? In what did they think that their unity, such as it was, consisted? In language, descent, or politics? What sort of unity did they in fact enjoy, and, insofar as it changed, did their perception of it change too? Which came first, political unity or a sense of unity? Finally, can we justify the degree of the break in continuity that is liable to be inferred from references to “the Anglo-Saxon period,” especially when it is contrasted, as it often is by British archaeologists, with a “medieval period” that began only in 1066? Did the identity of the people and their culture change as much in 1066 as the change of name implies?
The consideration of these questions here will start from the premise that medieval people seem to have envisaged their world as divided into “peoples” (gentes, nationes, populi) of common biological descent and culture who normally and naturally formed separate political units. By the twelfth century, though maybe not before the tenth, these political units were quintessentially thought of as kingdoms. It is important to remember that these assumptions about peoples and kingdoms are not quite the same as the assumptions about nations and states that many people hold today and that, unless we recognize them and allow them, will color our view of the past. In the Middle Ages, at least after the tenth century and perhaps earlier, it was assumed that a people who, as some kind of political unit, shared common customs and law—and quite often a common language, though the texts mention that less often—were therefore of common descent. Nowadays, on the other hand, it is often thought that people of common descent share a common culture and therefore ought to form a separate political unit. The medieval assumption was an unreasoned justification for the status quo; the modern belief is an often controversial justification or change. The modern ideas have therefore been sharpened and altered by controversy and abuse in a way that the medieval assumptions were not. Though medieval people perceived differences between “peoples” and felt collective loyalties to their own, we cannot assume without argument that their perceptions of identity and difference cor respond in all respects with modern perceptions of national and “ethnic” divisions, based as they are on modern ideas of popular government, nationalism, and race.[…]
One consequence of this line of thought is that one may go on to resolve some of the problems of the period by deducing that the so-called Germanic tribes of the Dark Ages probably formed much less tidy entities than is traditionally supposed and that there may have been comparatively few wholesale movements of groups that we can describe as tribes without grave risk of being misunderstood. Having suggested this, however, one has to concede that the migrations into England look like a special case.
In fact we do not know how consistently the Germanic-speaking invaders of Britain behaved like a group or felt themselves to be a group during the fifth and sixth centuries. We do not know what they called themselves or what others called them, if indeed they had any collective name. To the Roman authorities, those whom they called Saxons may have been particularly noticeable. Saxons, Scots, and Piets were the only barbarian invaders whom Gildas thought worth naming."
That does not necessarily mean that all the Germanic speaking invaders thought of themselves as Saxons or automatically allied themselves with Saxons against Britons, Piets, or Scots. By the eighth century, however, a sense of unity had somehow developed that enabled Bede to write in Latin of the gens Anglorum and, perhaps, to speak in the vernacular of the Angelcynn or Angeldeode — or both. Those people in other countries, meanwhile, who by then spoke of the inhabitants of eastern Britain as “Saxons” (perhaps as a continuance of the earlier Roman usage) seem, as the qualifications “English Saxons” or “Saxons of England” imply, to have meant by this much the same people as Bede meant by gens Anglorum.
Given the fluid and confused conditions that are likely to have prevailed through most of Britain in the fifth and sixth centuries, military and political conflicts may not always have followed “ethnic” lines: by the seventh century, when a sense of English unity is easier to postulate and explain, they did not. It may be a mistake to try to make sense of the fifth and sixth centuries by picturing the countryside as divided into British settlements, English settlements, and empty areas, which can be mapped by dating either archaeological finds or place-names and attributing them neatly to particular ethnic groups.
The implication of this argument—which is, of course, neither original nor provable—is that those whom we call Anglo-Saxons were not consistently distinguishable from everyone else. They were definable primarily by their military allegiance. Kings who called themselves (or whom Bede and others would later call) English or Saxon—although, incidentally, some of them bore British-sounding names—ruled areas that were therefore thought of, or later came to be thought of, as English or Saxon.
— Susan Reynolds: "What Do We Mean by “Anglo-Saxon” and “Anglo-Saxons”?", The Journal of British Studies, Volume 24, Issue 04, 1985, pp395–414.
The speculative reasoning is evident when Bede tells us a venerable story that cannot be true when we look at the creation of these entites and their naming:
Bede, perhaps inadvertently, conveys the impression that clearly delineated territories of West Saxons or Northumbrians, East Angles or Mercians, actually emerged in the course of the Anglo-Saxon settlement in Britain. In the context of events c. 600 or before he refers to the kings and kingdoms of the men of Kent, the East, South and West Saxons, and the Northumbrians.
Subsequently, the Alfredian chronicler clearly regarded Wessex as always having existed as the West Saxon kingdom under a consecutive succession of kings of the West Saxons. The chronicler simply conceived of Wessex in its ninth-century form as having sprung into being in the fifth and early sixth centuries, since when nothing had changed. Bede was doing much the same in the early eighth century. In the past historians have tended to follow suit and have regarded the heptarchic kingdom as securely established by the sixth century, if not earlier in some cases. An inflexible and somewhat anachronistic pattern has thereby been imposed on the historical development of these pre-Viking kingdoms.
The only Anglo-Saxon kingdom which is attested in a contemporary sixth-century record is Kent.
Gregory of Tours in his Frankish Histories, written in the late sixth century, twice refers simply to Kent and once to Kent as a kingdom. Documentation otherwise allows the existence of Bede’s principal kingdoms to be traced back in general only into the later part of the second half of the seventh century. The East Saxons are first mentioned by name in the extant records in a grant of land by Oethelred, kinsman of Saebbi, king of the East Saxons (CS 81:S 1171), in a late eighth-century text, the original of which probably belongs to 686–8. Their northern neighbours were known as the East Angles by 704–13 when the Whitby Life of Pope Gregory, which refers to them as such, was written. The regnal style ‘king of the West Saxons’ is not found before c. 760, but ‘West Saxon’ appears in an original text of a letter of Wealdhere, bishop of London, to Beorhtwald, archbishop of Canterbury in 704–5.
Similarly, the earliest charter to contain a reference to South Saxons is a grant by Nothhelm, king of the South Saxons in the period 688–705, in 692 according to the text of the charter itself (in what may, however, be a later addition) (CS 78:S 45). These names were certainly in use, therefore, by the late seventh or early eighth century; the question is whether they are very much earlier.
Bede includes in the Historia Ecclesiastica two conciliar documents from the second half of the seventh century, relating to the councils of Hertford in 672 (HE IV, 5) and Hatfield in 679 or 680 (HE IV, 17). Both are transcripts of the proceedings of the two councils and — unless Bede has modernized their wording — of great relevance to the study of the nomenclature of the Anglo-Saxon kingdoms. The preamble to the council of Hertford records the presence among others of Leutherius, ‘bishop of the West Saxons’, and Bisi, ‘bishop of the East Angles’, and records that proctors represented Wilfrid, ‘bishop of the Northumbrian people’. The record of the council of Hatfield is dated by the regnal year of Aldwulf, ‘king of the East Angles’. In the earliest records, however, kings are not given a geographical designation at all. Individual rulers were addressed in papal correspondence as ‘king of the Angles’, or as ‘king of the Saxons’.
In the 680s, Sigehere, whom Bede subsequently identified as a king of the East Saxons (HE III, 30:IV, 6), was only described in an admittedly suspect Kentish charter as ‘king of the Saxons’ (CS 89:S 233). Ine, king of the West Saxons, is styled ‘king of the Saxons’ in 701 (CS 103:S 243) and before him King Centwine in 682 likewise (CS 62:S 237), to whom Aldhelm of Malmesbury also referred as ‘king of the Saxons’ c. 690. On the inscription on his tomb in Rome, where he died in 688, Caedwalla was simply ‘king of the Saxons’ (HE V, 7). This evidence would suggest that terms like ‘East’ and ‘West’ Saxons may not long have been in common use before they appear in the late seventh or early eighth century. The failure of Bede to mention the Middle Saxons at all could indicate that the name Middle Saxon was not then of long-standing. Bede says that the West Saxons were formerly known as the Gewisse (HE III, 7) and it is likely that earlier names among the East, Middle and South Saxons and the East and Middle Angles were similarly discarded when they adopted geographically oriented ones. There is, however, an exception. Among more powerful rulers, the kings of the Mercians avoided similar categorization. They remained kings of the Mercians, the name signifying ‘boundary people’ or ‘people of the border’, and their bishops continued to be identified as bishops of the Mercians. It is curious that the Mercians never became the West Angles; it was the Magonsaete who were called West Angles.
What little evidence there is could suggest that it was a Canterbury terminology which imposed on the Anglo-Saxons the territorial designations ‘East’, ‘West’, ‘South’ and ‘Middle’. The records of the councils of Hertford and Hatfield, convened under Theodore, archbishop of Canterbury, are Canterbury records, and reveal that such territorial designations may already have been in use in Canterbury circles in the 670s. In the first decade of the conversion of the Anglo-Saxons to Christianity bishoprics were established near the power-bases of the local kings—at Canterbury, London, York, Dorchester-on-Thames— and their diocesan boundaries, vague and ill-defined in the beginning, fluctuated as the political circumstances of the local dynasties waxed and waned.
Bede says of Bishop Wilfrid that he administered the see of York as far as the power of King Oswiu extended (HE IV, 3). There may have been a need, therefore, to try to define more specifically than was native practice the territory over which a bishop had jurisdiction. The council of Hertford was concerned to declare against any bishop who intruded into the diocese of another. Bishops were to be content with the government of the people committed to their charge. The problem was to define such a people when the secular rulers were simply addressed as kings of the Angles or Saxons without distinction.
For some reason, the native names must generally have proved inadequate for the Church’s purpose, perhaps because they failed to signify changing political realities. It may be that the earliest bishops of Dorchester were known as bishops of the Gewisse, but the area around Dorchester was lost to the Mercians in the 660s and in 672 at Hertford the title of the bishop of Winchester appears to have been ‘bishop of the West Saxons’.
Why ‘West’ specifically? Viewed from Winchester, these Saxons could have been South Saxons, the South Saxons the East Saxons and the East Saxons the North Saxons. From Canterbury’s perspective, however, they were West, those of their neighbours towards Kent South, the Saxons to the north of the Thames East, those between the West and the East eventually Middle. The symmetry of it indicates a common Canterbury viewpoint.
The next stage would be to define the kingdoms in the same ecclesiastical terms. This stage had already been reached at Hatfield with the description of Aldwulf, for example, as king of the East Angles. If this reconstruction is correct, Aldwulf s kingdom was being defined for him in terms of the diocese of his bishop as perceived by the metropolitan church of Canterbury. Other kingdoms were also so defined across the later years of the seventh century until by the early eighth these probably relatively new designations— West Saxon, East Saxon, South Saxon, East Anglian, Northumbrian—were being universally popularized by Bede and firmly established in the political vocabulary of the heptarchy. Northumbria provides a good illustration of this. The northern ruler, Ecgfrith, king—in the Ecclesiastical History—of the Northumbrians (HE V, 26), had been styled ‘king of the Humbrians’ (rex Humbronensium) by those who drew up the record of the council of Hatfield (HE IV, 17), implying rule over a collection of territories astride the Humber.
Bede called him king of the transhumbrian regions in his History of the Abbots. As early as the council of Hertford in 672, however, Wilfrid, whose episcopal jurisdiction at that time was probably confined north of the Humber (see below, p. 95), was evidently styled ‘bishop of the Northumbrian people’ (HE IV, 5), and this was how the northern kingdom came to be finally defined. By the time of the writing of the Ecclesiastical History Bede was consistently referring to it as Northumbria throughout its history.
To avoid too anachronistic a portrayal of early English history, therefore, for the period before c. 700, rather than the familiar territorial names, the less specific eastern, southern and western Saxons, and eastern and northern Angles have much to commend them as sufficiently adequate for purposes of identification without the precision which the more familiar names impose.
— D. P. Kirby: "The Earliest English Kings", Routledge: London, New York, 22000. (pp20–22)
An easier to access description of the Northumbrian development (and highlighting again that mainly Irish sources describe some 'Kings of the North Saxons'):
— Neil McGuigan: "Neither Scotland Nor England: Middle Britain, C.850-1150", Dissertation, University of St Andrews, 2015. (PDF, hdl-identifier)
— Heinrich Härke: "Sächsische Ethnizität und archäologische Deutung
im frühmittelalterlichen England", Studien zur Sachsenforschung 12, 1999. (p109–122).
— Joachim Herrmann & Bruno Krüger: "Die Germanen. Geschichte und Kultur der germanischen Stämme in Mitteleuropa. Ein Handbuch in zwei Bänden", Vol 2, Akademie der Wissenschaften der DDR: Berlin 51988.
— Stuart Laycock & Miles Russell: "UnRoman Britain: Exposing the Great Myth of Britannia", The History Press: Stroud, 2011.
— Barbara Yorke: "Fact or fiction? The written evidence for the fifth and sixth centuries AD" Anglo-Saxon Studies in Archaeology and History, 6, 1993. (p45–50).
It is also the case that in the present state of knowledge it is impossible to distinguish archaeologically between a West Saxon and any other sort of Saxon.
We can no longer speak as confidently of the origins of Wessex as historians once felt able to do, […]
— Barbara Yorke: "Kings and Kingdoms of Early Anglo-Saxon England", Routledge: London, New York, 1997.
Our written sources are scarce and mainly mirror the myths of origin and myths of conquest for a largely illiterate culture as written down centuries later. Beda and Gildas cannot be taken literally as documentary evidence.
From those sources we often think of the Saxons, Jutes, Angles as settling in ethnically closed communities, replacing the local population. But archaeological evidence shows they were accompanied by Frisians, Goths, Huns, Rugians, Franks, Brukteri, Suevi, Alamans, and an early Scandinavian element. And all those continental newcomers settled intermixed with one another — and with the local population. The allegiance within any one of those territories affected was not by ethnicity, but by following the local leader. The Wessexians when we see them as inhabitants of an established and historical kingdom are therefore not 'the West Saxons'. It follows that looking for the equivalent 'North Saxons' in Nossex might be a fruitless task. Endonyms and Exonyms already diverged too much.
Those called 'Saxons' were by then seen as a more homogenous group. But they were so called by the Welsh, the Irish, the 'Italians', when they themselves were already calling their people Angli in parallel. Those 'Saxons' that went to more Northern parts of England most probably simply acculturated and assimilated into the newly emerging people, as did the others. By that time a naming of regions and principalities or administrative divisions came along that alluded to 'Saxons' in the last syllable, the regions to the North of Wessex, Middlesex and Essex retained their Saxon population elements but preferred another name. In the case of Mercia they did so apparently quite consciously. Our information does not allow to equate myths or late regnal and administrative terminology to earlier history and/or 'ethnic' developments.