Question : Is it true that if I get my period during the day, then I still have to complete my fast (even though I still have to make it up in the future)? What if I have ‘broken’ my fast in the past once my period started, ignorant about this ruling?
Answer : No.
It is necessary (wajib) to abstain for the rest of the day from food, drink, and sexual activity in the opposite case: if one was not fasting (e.g. because of menstruation or travel) and then the reason not to fast ends (e.g. one’s period ended, or one became resident). Not abstaining would be sinful, requiring repentance but not expiation.
In the case mentioned, when one’s period starts after one began fasting, it would not be permitted to continue fasting the rest of the day, and doing so would be sinful.
[Maraqi al-Falah; Hindiyya]