What is the ruling on the fasts of the questioner in previous years, given that he relied for starting and ending his fast on the timing of the Adhan in Cairo, while knowing that the time of the Fajr Adhan in his city (Zagazig) precedes that of Cairo?

If you ate after the Fajr (dawn) began, thinking that night still remained, then you must make up that day according to the majority of scholars if it becomes certain to you that Fajr had indeed begun. Otherwise, if there is doubt, you are not required to make up the day, because the original presumption is the continuation of night. What you mentioned about a two-minute difference according to the timetable does not necessitate making up the day due to the lack of certainty.