Is it permissible for a mother to inherit from her deceased, unmarried paternal aunt, given that her only brother (the mother's maternal grandfather) is deceased, and he has only one daughter, who is the mother, and there are no other relatives?

The niece (daughter of the brother) is considered among the relatives by blood (Dhawu al-Arham). Scholars have differed regarding their inheritance. Some, like Malik and Al-Shafi'i, do not grant them inheritance. Others, like Abu Hanifa and Ahmad, do grant them inheritance, provided there is no 'asabah (agnate heir) or a Dhawu Fard (Qur'anic heir) to whom the remaining share reverts. This latter view is the correct one, based on the Almighty's saying: (And those of [blood] relationship are more entitled [to inheritance] in the ordinance of Allah than [other] believers and emigrants) [Al-Anfal: 75], and the Prophet, peace and blessings be upon him, said: "The son of a people's sister is from among them," and "The maternal uncle is the heir of one who has no [other] heir." The situations of Dhawu al-Arham are three: if there is only one present, they receive the entire wealth. Thus, the full sister's daughter takes the entire wealth by ta'sib (agnatic inheritance). The half-sister's daughter (from the mother's side) takes one-sixth as a prescribed share (fard) and the remainder by رد (رد - return of the surplus). Based on this, the mother inherits all of her paternal aunt's wealth.