All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
If the children of this man are included in any of the eight categories who are entitled to receive Zakah and the owner of this money did not specify a certain party to which his Zakah should be paid, then it is permissible for that man to give this money to his children.
The criterion of giving a university student Zakah money is that he be included in any of the categories that are entitled to Zakah, such as being poor, in debt and so on while being unable to earn his living or to combine studying and earning a living. Furthermore, such a student should be intelligent and seeking a sort of knowledge that is needed by Muslims. If the children of that man have such qualities, then there is no sin on him giving them the money that he was entrusted to deliver to those who deserve it. However, the Zakah of his own money, if he has any, should not be paid to his children.