According to our present calendar and the most widely accepted chronology the year was 587.
Considering only the date of 607 given by Jehovah's Witnesses: it is quite incompatible with almost everything else we know.
One of the most prominent proponents of this 'theory' is Rolf Furuli, offering us his modestly named 'Oslo-chronology' in his book:
— Rolf Furuli: "Persian Chronology and the Length of the Babylonian Exile of the Jews Assyrian, Babylonian, Egyptian and Persian Chronology Compared with the Chronology of the Bible", R. Furuli: Oslo, 2003)
This work relies quite heavily on many quite 'original' observations, conclusions and cherry picking of evidence. It was reviewed as:
Once again we have an amateur who wants to rewrite scholarship. […]
Part of his redating is fairly modest: he accepts the beginning and end of Achaemenid rule according to the standard dating, and puts the beginning of Darius I’s reign only one year later than is conventional. He argues, however, that the first 11 years of Xerxes’ reign overlap with the last 11 of Darius, and that Artaxerxes I came to the throne in 475 BCE and ruled 51 years. (F. has indeed found the interesting fact that a couple of tablets have the years ‘50’ and ‘51’ for Artaxerxes, but he admits that overwhelmingly tablets make 41 his last year and none is found between 41 and 50, suggesting the obvious: a scribal error.) Gifted amateurs have sometimes revolutionized scholarship, notably M. Ventris and Linear B. But Ventris was willing to work with specialists such as J. Chadwick whereas F. shows little evidence of having put his theories to the test with specialists in Mesopotamian astronomy and Persian history. Perhaps the most telling point is his rather naive argument that the 70 years of Judaean captivity must be a literal 70 years of desolation of the land because some biblical passages make such a statement. A second volume is promised; we shall see if it is any more convincing.
— Lester L Grabbe: Review of "FURULI, ROLF, Persian Chronology and the Length of the Babylonian Exile of the Jews Assyrian, Babylonian, Egyptian and Persian Chronology Compared with the Chronology of the Bible, 1 (Oslo: R. Furuli A/S [firstname.lastname@example.org], 2003), pp. 251. n.p.", in: Journal for the Study of the Old Testament, 28(5), 40–58,'3. History, Geography and Sociology', 2004. DOI
An argument that rests entirely on word for word literal truth of every passage in the bible is a very weak one.
While Furuli's picking of 'evidence' is sometimes straightforwardly transparent – like when in chapter three he asserts that while the change of reign from Nebuchadnezzar to Amel-Marduk and Neriglissar is documented in tablet NBC 4897; because this contradicts F.’s chronology, he says it “cannot be used” – his most important argument rests the already mentioned on this page tablet VAT 4956.
And this tablet is egregiously misdated by JW-adherents and Furuli.
A more detailed analysis of some aspects and problems with the book, its methodology is here by Hermann Hunger, Vienna, Austria, author of " Astronomical Diaries and Related Texts from Babylonia, Vol. I: Diaries from 652 B.C. to 262 B.C.", Verlag der österreichischen Akademie der Wissenschaften: Wien, 1988)."
A layman's compatible analysis of the astronomical calculations and implications would read like:
The cosmic fingerprint doesn’t lie. Year 37 was 568 BCE, so Jerusalem was destroyed in Year 18, 587 BCE. Watchtower chronology doesn’t stand a chance.
— "The Astronomical Diary, VAT 4956", XJW Friends, 18 Feb 2018.
[…] three lunar eclipse tablets that establish Nebuchadnezzar’s reign: LBAT 1419, LBAT 1420, LBAT 1421. Even these are not the only ‘game in town’, but they are enough to provide dozens of absolute dates that prove Nebuchadnezzar’s 18th year, the year Jerusalem was destroyed, was 587 BC.
— VAT 4956
— John M. Steele and Annette Imhausen [eds.]: "Under One Sky: Astronomy and Mathematics in the Ancient Near East", Ugarit-Verlag: Münster 2002, pp421–428, we see F. Richard Stephenson and David M. Willis have in their chapter "The earliest Datable Observation of Aurora Borealis" en passant also evaluated the lunar data in VAT 4956 and come to the conclusion that the date 586/7 BC can be “confidently affirmed”.