بسم الله الرحمن الرحيم
If your father gave the money in the possession of your mother during his lifetime then your mother became its owner. And if your father did not make her its owner rather he died while the money was in his possession then the money became inheritance after his death and your mother shall get one eighth as her share, while you as well as any other heirs shall get their share in the rest amount. After all, whether your father gave the money to your mother during his lifetime and make her its sole owner or after the death of your father the property was divided and your mother got her share, in each case, the zakah of that money shall be due on your mother from the time she became its owner up to the time of completing one year provided it is equal to nisab or she became sahib-e-nisab in case of combining other nisab.
Allah knows Best!
Darul Uloom Deoband
This answer was collected from the official ifta website of Darul Uloom Deoband in India.