From Dr Timothy Patrick Donaldson
I've researched this, using some very helpful source materials from Rootschat discussion groups in 2018, in particular, transcriptions of Bishop John's grandfather's will, Roger Aylmer - https://www.rootschat.com/forum/index.php?topic=801335.0, and transcriptions of his cousin's will , Alexander Aylmer https://www.rootschat.com/forum/index.php?topic=800382.54 . From these, and other legal documents, including Frances Aylmer's will, I've constructed, what I think, is a reliable pedigree, of Bishops John's antecedents, and his relatives, and his relationship to Frances Aylmer, which I'd like to add to Geni (about 50 profiles in all).
Correct relationships are. Roger Aylmer of Tivetshall St Margaret, Wilby and Tannington d. 1497 - son John - son Bishop John. Then, same Roger Aylmer - son Edmund - daughter Frances c.1486-1540.
There were at least two Aylmer families in Norfolk in the late Middle Ages. One from Norwich and one from the Tivetshall St Mary/St Margaret area. Bishop John belongs to the Tivetshall branch, as stated in the extract from Encyclopedia Britannica in his Geni profile. Both Norfolk families, and the Irish branch, bore the same coat of arms so they must have originated from a common ancestor but I haven't found any documentation yet to show the connections; probably around the 1400's. Just for completeness there were some Alymer families in the nearby counties of Suffolk and Essex, and maybe a third Norfolk one. All probably connected, but it will take more research to establish that or not. There are some documents which are held by the Norwich registry office which I haven't got yet, but they might help.