Praise be to Allah.
Giving zakah to relatives who are entitled to it is better than giving it to those who are not your relatives, because giving charity to relatives is both charity and upholding the ties of kinship. The Prophet (peace and blessings of Allah be upon him) said: “Charity given to a poor person is charity, but charity given to a relative is two things, charity and upholding the ties of kinship.”
Narrated by al-Nasaa’i, 2581; al-Tirmidhi, 658; classed as saheeh by al-Albaani in Saheeh al-Nasaa’i, 2420.
But if these relatives are among those on whom you are obliged to spend, but you give them your zakah so that you can save money, then that is not permissible.
But if your wealth is not sufficient to spend on them, then there is nothing wrong with giving them some of your zakah. Similarly, if they are in debt and you pay off their debts from your zakah, there is nothing wrong with your doing that, because a person is not obliged to pay off his relative’s debt, so if he pays it off from his zakah then that is fine. Even if it is your son or your father who owes a debt to someone and cannot pay it off, it is permissible for you to pay it off from your zakah.
From the fatwas of Shaykh Muhammad ibn ‘Uthaymeen (may Allah have mercy on him). Fatawa al-Shaykh Muhammad al-Saalih al-‘Uthaymeen, 1/461.