Should I heed my father's advice to abandon the votive fast I pledged, which is to fast on Mondays and Thursdays?

Undertaking a vow is disliked (makrooh), but you must fulfill it as long as you have made it. You are not obliged to obey your father in his prohibition of you fulfilling this vow, due to the saying of the Prophet, peace and blessings be upon him: "Obedience is only in what is good," and "There is no obedience to a creature in disobedience to the Creator."