During the Crusade of Varna, the Ottoman sultan Murad II, Kasim Pasha the beylerbey of Rumelia, and Turahan Bey the governor of Thessaly, burned down the city of Sofia retreating from the Crusaders. However, what if they did so too late, and the Crusaders trapped them in the city? The Ottoman sultanate would pass to Mehmed II who was only 12, and the two main military leaders of the Ottoman Empire in Europe, would be dead. In this case, the Ottomans would be placed in a dire situation.
At the same time, the Mamluks and Karamanids raided the Ottoman territories in Anatolia. They were pushed back and accepted an Ottoman ceasefire. But if the Ottoman army is decimated in Bulgaria that might change.
Meanwhile, the Byzantines had an Ottoman pretender, Şehzade Orhan Çelebi, who was so loyal to the Byzantines that he fought on their side against the Siege of Constantinople in 1453. If Hunyadi wins the Crusade, then the Polish and Hungarian contingent will grab territory from the Ottomans in Europe. Thessalonica or at least some territory will be granted to the Byzantines, while the Venetians and Genoese will take their share. The Karamanids would devastate Anatolia. At this point, the Byzantines can unleash their pretender, Orhan Çelebi, on the Ottomans.
Mehmed II is killed by nobles trying to take the throne, or by Orhan Çelebi. Orhan takes the throne as a Byzantine puppet. From here, the Byzantines can incorporate the Ottoman Empire as a vassal state and influence it. Some sultan in this completely demoralized, restricted Ottoman Empire can convert to Christianity, either Orhan or a later pro-Byzantine noble. By that point it might be the 1500s. In any case, from here the Christian Ottoman empire perhaps in union with the Byzantine empire, can begin to recover although in a completely different form than the original empire.