Who inherits a father who has children born out of wedlock, and is it permissible for him to grant a gift to his two daughters in a way that prevents his brothers from inheriting?

The child of an adulterer is not attributed to him according to the majority of jurists, so there is no inheritance between them. However, some scholars, such as Sheikh Al-Islam Ibn Taymiyyah, are of the view that the adulterer's child born to the adulteress is attributed to him if she was not married to another man at the time, and in this case, inheritance is established.

As for the pregnancy your mother had during marriage, the child's lineage is attributed to your father unless li'an (oath of condemnation) occurs, and the child inherits from him in the event of his death.

If your father passes away and there is no male child, the daughters inherit two-thirds, and his brothers take the remaining one-third. However, if he has a male child, the entire inheritance is divided, with the male receiving the share of two females.

It is not permissible for your father to gift you anything with the intention of disinheriting his brothers, as this transgresses the limits set by Allah. A gift that is not taken possession of is not valid unless the remaining heirs agree, because it is in the ruling of a bequest to an heir.