The Verdict: Not eligible
There is no route to Turkish citizenship for descendants of families who left the Ottoman Empire or early Republic, or who were stripped of nationality, so you would need another path such as naturalisation or investment.
Turkish law has no Ottoman-descent route and no restoration scheme for descendants.
Article 43 of the Turkish Citizenship Law lets a person who was personally stripped of nationality under the 1928 law, or who lost it under certain grounds of the 1964 law, apply to take it back without living in Turkey. It applies only to that person, not to their children or grandchildren. Under the 1964 law, people who left Turkey by the end of 1930 on passports barring return were also treated as having lost nationality, and nothing restores their descendants.
If one of your parents or grandparents was still a Turkish citizen when their child in your line was born, choose that answer instead: the claim would then be ordinary descent. Otherwise, naturalisation after five years living in Turkey, marriage to a Turkish citizen, and investment are the routes; our other Turkey quizzes cover them.