Is it permissible for a father to give his married daughter a portion of his Zakat to cover her university tuition fees, knowing that her husband cannot afford to pay these fees?

Your father is not permitted to give you zakat from his wealth as long as your husband provides for your expenses. University education is not originally among the categories for zakat disbursement, unless the conditions mentioned by jurists for the permissibility of giving zakat to a student of knowledge are met.