Should I make up for the fast of the day on which I ate a date with the Fajr اذان (call to prayer), thinking it was the first اذان (call to prayer)?

If a fasting person eats dates, believing that night still remains, and then it becomes clear that the eating occurred after the second call to dawn prayer (adhan al-fajr al-thani), which is called after the true dawn (al-fajr al-sadiq) has appeared, then there is a difference of opinion among scholars regarding the validity of his fast. The more cautious approach is to make up this day (qada') in order to avoid the disagreement.