What is incumbent upon me due to my father not fulfilling the vow he made while my mother was pregnant with me, and does that affect me?

The ruling on a vow is determined by the intention of the one making it: If the intention is to show joy without an act of obedience, and it is free from forbidden acts, then it is a permissible vow that does not require fulfillment, and an expiation for breaking an oath is due. If it contains forbidden acts, then it is a vow of disobedience that should not be fulfilled, and an expiation for breaking an oath is due. The Messenger of Allah (peace and blessings be upon him) said: "Indeed, a vow is an oath; its expiation is the expiation of an oath." And "There is no fulfillment for a vow that involves disobedience to Allah." If the intention is an act of obedience, such as thanking Allah by providing food, then it is a vow of obedience that must be fulfilled. A'ishah (may Allah be pleased with her) narrated that the Prophet (peace and blessings be upon him) said: "Whoever vows to obey Allah, let him obey Him; and whoever vows to disobey Him, let him not disobey Him."

A son can fulfill a vow or its expiation on behalf of his father with his permission. Whoever does not fulfill a vow or its expiation, it remains a debt upon them. However, the son is not obligated by anything from his father's vow, for "every soul earns only on its own account, and no bearer of burdens will bear the burden of another."