السلام علیکم ورحمة الله
A person has one paternal brother and one maternal sister. Is it permissible for his paternal brother to marry his maternal sister?
بِسْمِ اللهِ الرَّحْمنِ الرَّحِيْم
In the name of Allah, the Most Gracious, the Most Merciful
Allāh says: "Prohibited to you [for marriage] are your mothers, your daughters, your sisters, your father’s sisters, your mother’s sisters, your brother’s daughters, your sister’s daughters, your [milk] mothers who nursed you, your sisters through nursing, your wives’ mothers, and your step-daughters under your guardianship [born] of your wives unto whom you have gone in. But if you have not gone in unto them, there is no sin upon you. And [also prohibited are] the wives of your sons who are from your [own] loins, and that you take [in marriage] two sisters simultaneously, except for what has already occurred. Indeed, Allah is ever Forgiving and Merciful."
The generality of the verse makes it applicable not just to full siblings (i.e. those who share both biological parents), but also to half-siblings (i.e. those who share one biological parent). However, this does not apply to stepsiblings (i.e. those who do not share any biological parents). Therefore, so long as your paternal brother and your maternal sister do not share even one biological parent in common, they will not be considered maḥram to each other, and it would be permissible for them to get married to each other.
Only Allah knows best
Written by Shaykh Umer Khan
Checked and approved by Mufti Mohammed Tosir Miah
Darul Ifta Birmingham