If I understood you well, you ask about the legal status of children gathered through devşirme, slave trade etc.

In the Imperial Household (that is, at the court), only the sultan, his family and relatives, teachers, religious instructors, prayer leaders, doctors, mutes, dwarves and wrestlers were legally free. Everybody else was theoretically a slave. As you may conclude from this, being a slave did not greatly affect those on the court; for at the Ottoman society one's rank in society did not depend on the slave vs free man dichotomy, but on the status of his family and household. Slaves in wealthy households were in greater status than free but poor men. And it was deemed the greatest honor to be a slave of his household. The only better position would've been the very position of the sultan. The Grand Vizier was also technically slave to the sultan. That's why the sultans were able to execute them - as their own slaves.