بسم اللہ الرحمن الرحیم

الجواب واللہ المعین

It is not right for a father to give Zakat to his son and giving it to him does not discharge him of the responsibility of paying Zakat, However, for the sake of convenience in such cases, the scholars have come up with the idea that the person eligible to pay zakat, pays it to a deserving person and asks him to pay that amount to his son for the sake of Allah, then that trick is permissible, and Zakat will be paid to his son.

In addition, if the wife of the son is entitled to Zakat, then Zakat can be given to her and thus the need can be met.

فقط واللہ اعلم بالصواب