Sabbatai Zevi is sacrified by the Sultan even after converting to Islam. His followers are persecuted all over Ottoman Empire and are expelled from the OE fleeing to the nearest Jewish-friendly cities, mostly Italy, like Livorno, Pisa, Venice, etc.
After his conversion and sacrifice a considerable number of Muslim Turks converted to Sabbateanism and are expelled with the Jews. These Messianic Muslims establish themselves mosly at Livorno where they speak a Italkian/Ladino mix with a great Turkish substrate.