Woke up early to have something to eat and drink before the taanis. Was told that daybreak was around 4 am. after eating at 3:45 became aware that daybreak was at 3:36. Can I complete the fast as usual.
Even after eating, there is an obligation to complete the fast (Orach Chaim 568). You should say aneinu in davening, but should avoid receiving an aliah (Mishnah Berurah 568:2).
The Maharil writes that after eating on a fast day, one should fast an extra three days. However, this is not cited by the Rema, and Magen Avraham (568:4) writes that one does not need to fast extra days.