What is the ruling regarding the days the questioner fasted, on which she would have suhoor until the adhan of Fajr finished, knowing that she does not remember these days or their number, and how should she make them up?

It is not permissible to eat or drink after the dawn breaks, for Allah Almighty says: "And eat and drink until the white thread of dawn becomes distinct to you from the black thread [of night]." (Quran 2:187). If the muezzin calls the adhan after the time has entered, one must stop immediately upon hearing the adhan, not during it.

What happened with you, eating after the dawn adhan, is considered breaking the fast and necessitates making up the days that occurred after puberty. As for what happened before puberty, there is no making up for it. You must make up what you believe will clear your conscience. There is no sin upon you for your ignorance of the ruling and your following your father, and there is no expiation for delaying the making up; rather, only making up is required of you.