Siegfried Mekler (1852–1912) was an Austrian classical philologist. The Österreichisches Biographisches Lexikon has an entry. To put it bluntly: he was a school teacher for Latin and Classical Greek, did some scholarly research in his free time and gained at least some recognition with the adaptation of ancient poems. For his academic field and at his time, it was quite common to publish in Latin, even if the texts he wrote about were Greek – it just was the common language of scholars of antiquity.
In 1902, he published a book Academicorum Philosophorum Index Herculanensis. The title probably translates best to An Index to the Philosophers of the Academy from Herculaneum, and it is part of the early attempts to make sense of the Papyry of Herculaneum, the heavily-scorched scrolls found in 1753 in a villa in Herculaneum, when it was excavated from the ashes of the 79 AD eruption of Mount Vesuvius.
In the preface of the book, he identifies the scroll he is concerned with as titled
'Incerti auctoris liber, cuius titulus non superest', ab
Ioanne Bapt. Casanova anno proximi saeculi octave evolutus...numero 1021 insignitus
'A book of unknown authorship, whose title has not survived' (1), unrolled by Giovanni Bapt. Casanova, around the year 1800...with signature 1021.
The scroll (or rather, the drawing of that scroll) is available online from the Biblioteca Nazionale di Napoli as a scan. Its frontpage lists several people who worked on it: Genaro Casanova opened the scroll, Guiseppe Casanova in 1811 and Carlo Malesci in 1840(?) copied its contents to this facsimile, and editions are available by "C.A.I. Mekler, Academicorum Philosophorum index Herculanensis" beside another, later one. This seems to ascertain the identity of the scroll Mekler's book is about.
The scroll was understood to basically be a list/table/index of the philosophers of the Platonic Academy. I am not completely sure about my translation, so I'd appreciate any further help:
Cuius effigiem cum Itali in Collectionis Alterius tomo primo sollerter quidem arte chalcographa exceptamquovis tamen interpretemento carentem edidissent, felicissimo Leonardi Spengelii acumine effectum est, ut litterarum veluti nullo consilio glomeratarum farrago, cui ille Academicorum philosophorum πίναχα inesse agnoverat, documenti speciem indueret vere humani(3).
(3) Spengel Philol. Suppl. II 5 p. 535: 'Wir haben hier...nichts geringeres als eine angabe der diadochen der akademischen schule'. primium illum conatum, cui laudem suam Bücheler p. 3 non detraxit, Comparetti 'assai leggermente et in fretta' ait susceptum, paulio iniquis, ut mihi quidem videtur, iudicans Relax. sui papiri ercol. (Atti d. R. Accad. d. Lincei S. III, v. V  p.163).
The Italians had published a reproduction in the first volume of the Alterius Collection, skilfully engraved, but lacking in any interpretation. Fortunately, this was achieved with the most successful acuity by Leonard Spengel, who acknowledged this mass of letters clustered together as if without any design, to be a table of the Academician philosophers and gave the document the appearance of a truly human one (3).
(3) Spengel Philol. Suppl. II 5 p. 535: 'Wir haben hier...nichts geringeres als eine angabe der diadochen der akademischen schule' (What we have here...is nothing less than a description of the diadochs of the academic school). That first attempt, from which Bücheler p. 3 did not detract, was found by Comparetti to be 'assai leggermente et in fretta' (very light and in a haste), somewhat unfairly, as it seems to me, judged by the herculanean papyri of Relax. (Atti d. R. Accad. d. Lincei S. III, v. V  p.163).
What exactly it is Alice Riginos found in that book, how exactly it relates to the biography of Plato is not clear, as your question contains barely enough information to figure out even that it was her book that cited this old edition of a scroll.
Papyri.info has a database entry for the scroll:
- Title: P.Herc. 1021
- Work: Philodemus, Academicorum Historia
- Content: Philodemus; syntaxis ton philosophon (Comparetti) index academicorum (Obbink)
- Reference Edition: 83645. Tiziano Dorandi, Filodemo, Storia dei filosofi (.) Platone e l’Academia, (Napoli 1991).
The full transcript of the scroll is cited at the bottom of the page, together with available sketches and engravings.
Following a few other links, it turns out that the original scroll was the subject of the 2019 experiment to use infrared imaging to reveal its content.
The scroll is a rough draft of a history of the academy founded by the philosopher Plato — written by another philosopher, Philodemus...
What they found are bits of text that Philodemus wanted to insert into his book, such as quotes from other sources he was considering using in the history. Classicist Kilian Fleischer from the University of Würzburg, who is putting together a new edition of Philodemus' history using these images, says it provides a unique view of an ancient philosopher's writing process.
"We have here more or less the only case where we can really see how an ancient author worked and composed his book," Fleischer says. "We can see he made notes — insert this later, insert this and this, and skip this and this for the final version and so on."
The full scientific report is here.