Is Zakat on money due on a savings account for which my father did not pay Zakat in previous years when he was depositing into it, knowing that the account is in my name?

Zakat (definition) is obligatory on the wealth of a minor according to the majority of scholars, provided its conditions are met, and the guardian is responsible for disbursing it. If your father did not disburse the zakat on your wealth, he has sinned. After you reached puberty, you became responsible for disbursing the zakat on your wealth, so you must verify with your parents. If you are not certain that it was disbursed, then you must disburse the zakat for the previous years if the wealth reached the nisab (definition), because one's liability is not discharged except with certainty.