Praise be to Allah The Lord of the Worlds.
It is permissible for the father to give his poor son, who is able to make a living, from the Zakah of his money if the income of the son doesn`t cover his basic needs and those of his family. This is because the father isn`t obliged to support the healthy, adult, sane son. It is stated in the book: "The father isn`t obliged to provide for his son who is able to make a living, which suits his social and financial status."{Hashiyat Al-Baijoori, vol.2/ pp..192}.
The Sharia maxim in this regard states: "The father isn`t permitted to pay from the Zakah of his money to those whom he is obliged to provide for." Al-Ramli [May Allah be pleased with him] said: "One who receives enough provisions from an ascendant or a descendant (or husband)…….is neither poor nor needy, and this is according to our, Shafie, most correct opinion. However, it is permissible to give such a person on grounds other than being poor and needy."{Nehayat Al-Mohtaaj ela Shareh al-Menhaaj, vol.6/pp.154}. Accordingly, it is permissible for the father to give his son from the Zakah of his money if the son is a debtor. And Allah The Almighty Knows Best.