All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is permissible for a father to single out some of his children in gift-giving if there is a legitimate Shariah reason for that and it isn`t his intention to deprive his other children from the inheritance. Amongst these reasons is that the favored child is poor and needy while the rest of his brothers aren`t, he is unable to rely on himself, he is a student, and the like. However, it is disliked to give a gift to one child for no need or clear reason, and not give to others.
Al-Shirbini says: "If the children are equally in need or in no need, then it is disliked to single out one of them in gift-giving and not give to others. Otherwise, this isn`t disliked. The evidence on this is that the companions have favored some of their children over others in gift-giving. For example, Abu Baker (May Allah be pleased with him) favored his daughter Aisha, Omar (May Allah be pleased with him) favored his son Asim. However, it isn`t disliked not to give a gift to the rebellious and disobedient child." {Moghni al-Mohtaaj, vol.3/pp.567}. And Allah The Almighty Knows Best.