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.
There is no impediment, under Sharee‘ah, to give the Zakah of your property to your son, since you are not obliged to spend on him. Zakah is forbidden to him upon whom you are obligated to spend; and your poor son is not among those upon whom you are obliged to spend. That is because he has attained the age of maturity and has become capable of earning his living, however, he does not gain enough to suffice him and his children. Ibn ‘Abbaas said: “If they are your relatives upon whom you are not obliged to spend, then, give them out of the Zakah of your property; and if you are obliged to spend on them, then, do not give them anything from it. Do not assign the Zakah of your property to anyone upon whom you are obliged to spend.” [Al-Athram in his Sunan]
Allaah Knows best.