This is a strange discussion. Arabs besieged Constantinople in the 7th and the 8th centuries and could have taken the city either time.
Then after Mankizert and what could only be described as a Byzantine collapse, the Seljuk Turks established a sultanate across from the Bosphorus and were only pushed back, and only into the interior of Anatolia, by the First Crusade. You could easily either not have the First Crusade or a more complete Byzantine collapse.
Then of course you have the Ottomans holding both Anatolia and the Balkans in 1400, with the Byzantine "empire" basically consisting of a few outposts, and about to take Constantinople when Timur showed up.
Even after the Battle of Ankara, you just need the Ottomans to rally and not split into small emirates, and then for Hungary to do worse than it did. Hungary eliminated every emirate but Edirne, and Edirne was so weakened that they had to sell Gallipoli to Venice.
Even then you need Carlos I/ Charles V not to be persuaded (he had alot on his plate) to send that expedition to the Straights for prestige reasons.
Even have the Council of Florence fail to end the Great Schism would be enough of a POD.