Only two of the people above are originally turks according to to wiki you posted
ali qushji is persian from Samarkand and Bukhara witch are both persian cities with majority Tajiks papulation
Haj bektash is not Turk he was born in nissapuor according the wiki he is sayyed who is desented from musa al kazim wich means he was arab from quraish from banu hashim
Haj Bektash Veli has more Turkish origin sources in his Wiki article and he's also listed under Turkish people. The same goes for Ali Qushji. So what if he's from Iran? Iran was already full of Turks in that time.