Byzantium's last historical Emperor was Constantine XI Palaeologus, but in this scenario he was succeeded by my own emperors. Keep in mind, this is a alternate history with my own imagination added into.
Constantine XI defends Constantinople from the invading heathens.
Constantine is dethroned, leading to a new dynasty, the Basiuelus dynasty, with Emperor Alexander "the Noble" at its head.
After a long period of war with the Ottoman Empire, Emperor Alexander manages to take back most of the land in Greece from the Ottomans.
The war ends, and after a brief period of peace, Alexander, with no direct heir dies. Alexander left the throne to his father when he died, but his father, Arcadius II, had recently died as well. With both the Ottoman Turks and Bulgaria claiming the throne, a succession war broke out. What people didn't know however is that there was an heir, his wife. His wife, Constantina "the Brave" fought with him, but in the entire time they didn't have an heir. The throne was given to her, and much to the dismay of the Ottoman Turks and the Bulgarians, the succession war ended.
Constantina attempts to take back Anatolia from the Ottomans, but fails and is killed in the process, leaving her son, Theodosius I, to take throne.
1480 is a massive time for the Byzantine empire, because Theodosius I was a Catholic, where as his mother and all his previous heirs, were Greek Orthodox. Theodosius I eventually converted after a religious civil war was placed, and though he won, to avoid further conflict he converted to Greek Orthodox.
MORE SOON! (please don't edit this with your own stuff, guys...)