Ash-Shaykh Muqbil rahimahullah clarifies in the following audio that it is permissible to give one’s zakaat to his own needy brother or own his needy sister if they have separate incomes from each other and while they don’t live under the same roof together.
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Ash-Shaykh Bin Baaz rahimahullah was asked the following question:
“Is it permissible for me to give Zakah (obligatory charity) due from my money, or Zakatul-Fitr (obligatory charity paid before the Festival of Breaking the Fast) to my underage brothers and sisters who are being brought up by my mother after the death of our father (may Allah be merciful to him)? Is it permissible to give such Zakah to my brothers who, though they are not underage, I feel are in need of it even more than other people? Should I pay them such Zakah?”
“Paying Zakah to relatives who are entitled to it is better than giving it to those who are not your relatives. Charity given to relatives is both charity and upholding the ties of kinship, unless these relatives are those on whom you are obliged to spend, in which case giving Zakah to them in order to free yourself from the obligation to spend on them is not permissible. If it so happens that these brothers and sisters whom you have mentioned are poor, and you cannot afford to spend on them, then there is nothing wrong with your giving them your Zakah. Similarly, if these brothers and sisters owe debts to people and you pay off their debts with your Zakah, there is nothing wrong with you doing that. That is because a person is not obliged to pay off the debts of his relative, so if he pays them off with his Zakah, that is something for which he will be rewarded. Even if it is your son or father who owes a debt to someone and cannot pay it off, it is permissible for you to pay it from your Zakah, i.e., it is permissible for you to pay off your father’s debt from your Zakah and it is permissible to pay off the debt of your son from your Zakah, so long as the reason for this debt is not to obtain money for maintenance that it is your duty to pay. If the reason for it is to obtain maintenance which is your duty to provide, then it is not permissible for you to pay off the debt from your Zakah, lest you use this as a trick to get out of spending on those on whom you are obliged to spend, i.e., forcing them to resort to incurring debts and then you pay their debts off with your Zakah. And Allah knows best.”
.زلا يستطيعان قضاءه ؛ لأنهما داخلان في قوله سبحانه: إِنَّمَا الصَّدَقَاتُ لِلْفُقَرَاء وَالْمَسَاكِينِ  . وبالله التوفيق
Note: Ash-Shaykh Bin Baaz rahimahullah restricts the permissibility to if the person has no capability in paying off the debt. It is not correct to pay the debt on behalf of the person with the intention of zakaat while the person himself is capable of paying it off. This is similarly stated by Shaykh Muhammad bin Saalih al-Uthaymeen rahimahullah.
Also some have mentioned that from its conditions is that the debt should be a heavy burden upon the person taken from the word الغارم in the ayah.
من أغرمته ديونه
“His debt has been a heavy burden on him.”
AbdulFattaah Bin Uthman