I am married with the daughter of my brother in-law but my sister is a half sister who is not from the same father like me, and her father died. I fathered a son from this wife, and he wants to marry the daughter of my sister, this means that the daughter of my sister is a sister of my wife from father's side and not mother's side. The question is: Is this marriage permissible?

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. We ask Allaah to exalt his mention as well as that of his family and all his companions.

It is not permissible for your son to marry the daughter of your sister from the mother's side, as she is his maternal aunt, as your wife is a sister for this girl from father's side. Allaah Says (what means): {Prohibited to you [for marriage] are your mothers, your daughters, your sisters, your father’s sisters, your mother’s sisters.}[Quran 4:23].

Allaah Knows best.