Won Preveze war against Doria's navy in 1538 making Ottomans the only authority in Mediterennean till 1571 Inebahti war. His father was a "timarli sipahi" named "Yakup" from Eceabat-Canakkale and being granted soil in Midilli (Lesbos), and her mother is told as a christian named Katalina according in some western sources, me not knowing if based on objective info or not. You should have read from them. You probably know what" timarli sipahi" is. Ignoring very rare exceptions, as law only Turkish soldiers (not christian conversions like janissaries, or other muslim tribes) who took role in conquering new lands were granted with some soil with people and villages on it, being responsible to take care of that land and collect tax, and train and feed soldiers given under his rule, and joining army with their men in war time, etc. Their titles, privileges and duties were passing to their sons. As the island was conquered in 15th cen., it is certain that Hayrettin was son of such a sipahi. He tells much about his father in his own memories. His brothers were pirates too, leaving their fatherland and joining Hayrettin in Algeria which he conquered himself with his crew in 1516, but all of them being killed in young age in wars against Spanish and Italians.(I strongly recommend all to read his memories if translated into English. He writes much of the chronicles and adventures of plundered ships and towns one by one, envolved battles, sieges, voyages enormously detailed and fast,cheerful, adventurous but not bloody manner. I guess must be the best pirate book on world). So, he is Turkish father and perhaps christian for her mother.would you get proud with the situation and prefer to accept his mother as Greek originated, depends on you
