All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
The daughter of the brother does not inherit her paternal aunt; and the daughter of the sister and son of the sister both do not inherit their maternal uncle.
The evidence is that the Sharia did not make them heirs; it is the Sharia that determines whether or not a person is an heir. So if Allah made a person an heir in His legislation, then we make him an heir, and if Allah did not determine a share of inheritance in the Sharia for a person, then we do not make him an heir [he does not inherit].
The rule in inheritance is that every person who is related to the deceased through a female does not inherit, with the exception of three:
1) A grandmother from the mother’s side [the mother of the mother].
2) Half-brothers and half-sisters from the mother’s side.
3) The ‘Asabah in case of the woman who freed her slave (and then he died leaving an estate); the ‘Asabah is the heir who does not have a determined share in the inheritance, so he/she gets the remainder of the inheritance after the heirs have taken their legitimate and fixed shares.
Allah knows best.