Is it permissible to pay a son's accumulated apartment installments from Zakat money to meet his needs and the needs of his family, in the event that his income is insufficient to pay these installments?

It is permissible to pay for your son's apartment from your Zakat (definition) al-mal if he is in debt, because he is considered one of the gharimin (those in debt), and the gharimin are one of the eight categories of Zakat recipients mentioned in His (the Almighty's) saying: "Zakat expenditures are only for the poor and for the needy and for those employed to collect [Zakat] and for bringing hearts together [for Islam] and for freeing captives [or slaves] and for those in debt and for the cause of Allah and for the [stranded] traveler - an obligation [imposed] by Allah." [At-Tawbah (definition):60].