Assalaamu alaykum. Dear Sir, is it permissible to spend zakah money on my father's second wife's children for their studies. They are still dependent and studying and my father passed away 18 months ago. Please advise

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 is His slave and Messenger. 

If the children of your father's wife are not your brothers from your father’s side, then there is nothing wrong for you to pay zakah to them if they are poor or destitute.

However, it is a condition when paying the zakah for their studies that the field of study must be Islamic, as the jurists restricted giving the zakah to the seeker of knowledge who studies Islamic studies and not the one who studies worldly knowledge.

The Fiqh Encyclopedia reads, “The scholars agreed that it is permissible to give zakah to the seeker of knowledge; the Hanafi, Shaafi'i, and Hanbali Schools explicitly declared this. This is also what can be understood from the view of the Maaliki School. The jurists singled out the permissibility of giving zakah to the student of Islamic knowledge only.” 

Shaykh Ibn ‘Uthaymeen said, “The student of knowledge who dedicates himself and his time to acquiring Islamic knowledge, even if he is able to earn his own living, it is permissible to give him from the zakah because seeking Islamic knowledge is a kind of jihaad for the sake of Allaah. But if the student was devoted to learning a worldly field of knowledge, then it is not permissible to give him from the zakah money.”

However, some scholars are of the view that it is permissible to give zakah to a seeker of worldly knowledge if he is seeking knowledge that is among the communal obligations.

However, if the children of your father's wife are your siblings, then we must look at whether or not you are Islamicly obliged to spend on them. If you are not Islamicly obliged to spend on them, then it is permissible for you to give the zakah of your money to them for their studies with the mentioned condition that the field of their study must be Islamic.

If spending on them is an obligation on you (according to Islamic law), then it is not permissible for you to give zakah to them, but you must, rather, spend on them. The expenses of their studies, if they do not have money, is on obligation on the person who is Islamicly obliged to spend on them. The Shaafi’i scholar Al-Khateeb Ash-Shirbeeni said in Mughni al-Muhtaaj, “The guardian must discipline the children (under his guardianship) and educate them regardless of whether he is a father, or a grandfather, or a trustee, and the fees for this are to be taken from the money of the children, and if they have no money, then this should be paid by the one who is Islamicly obliged to spend on them.”

The scholars who are of the view that it is an obligation to spend on one's siblings set some conditions for it:

Firstly: that they are poor and have no money and no earning.

Secondly: that the brother who spends on them has surplus money beyond his own expenses and his dependents' expenses. If the conditions are met, then you are Islamicly obliged to spend on them and it is not permissible for you to pay your zakah to them.

Allaah knows best.