Am I obligated to pay Zakat on money my father deposited for me since my childhood, over which I had no control, and I do not know whether my father paid Zakat on it or not, especially since I do not know the exact amount of this money?

If you know that your father did not pay zakat on the aforementioned money, then you must pay it for all the past years. Otherwise, you are not obligated to pay it. However, it is better to pay it as a precaution if you suspect it was not paid, while striving to estimate the wealth to pay the required amount.