While not a direct or complete answer to your question, I think this earlier thread from /u/RexSuiciae will be of much interest. Rex shows how the myth of Prester John was less about a specific geographic region in the cartographic sense, and more about a liminal kingdom in the imaginative sense--a place "on the edge" or just beyond it.

To provide a bit more context from the "what mediecval people knew (accurately or not)" angle:

Medieval Latin Europeans certainly had ample legends of apostles going "East" to evangelize after the great dispensation described in Acts. Thimas Aquinas cites events from some of them authoritatively in the Summa theologica, for example. And as Paul Freedman shows, "the East" was, again, a powerful and purposefully vague power in the medieval spatial imagination.

One of our late antique specialists would know much better than me the current state of research on Nestorian Christian missionaries towards Tibet/China (although there were in fact Church of the East believers who became Mongol queens...but it's an open question whether our monk and cleric scholars would have considered the, Christians or heretics) and Thomas Christians in India. But this doesn't show up explicitly in medieval western sources, except insofar as the legends of apostles going east, working miracles, converting kings.

While other commentators here have addressed the Prester John legend in the 12th century, I can supply a revealing anecdote from the thirteenth. Marco Polo in his journey through the Mongol Empire to the court of Chinggis Khan's grandson Kublai Khan identified Prester John with Toghrul of the Kereit tribe, known better as the Ong Khan. Toghrul had been a Nestorian Christian and leader of one of the most powerful tribes on the Mongol steppe, and an ally of Chinggis Khan until Toghrul betrayed him, leading to his eventual defeat at the hands of Chinggis. Polo essentially says, "All those theories of who Prester John is are wrong, this fellow here was he, and the Mongols have already defeated him!" Presumably because of the fact that Toghrul was Christian he was therefore identified as Prester John by Polo.

This is revealing as it demonstrates a key point of the Prester John legend, in that he was associated with whomever, and wherever, Europeans felt was possible. However, it was based on theories, such as stories of Christian Kings (in the case of Toghrul here, a powerful Christian lord much farther East than Marco would have thought possible, and therefore has! to be the Prester John of legend) or of non-Muslim armies defeating Muslims in battle (if they aren't Muslim, and are fighting Muslims, they must Christians! essentially) rather than conjuring him out of nothing.

Edit: spelling