Is it permissible for a father to favor some of his children in giving without the others, and would he incur sin for that? And what is the ruling of Sharia on the dispute that arises among children due to the father's favoritism of one of them in material gifts?

The preponderant view is the obligation to equalize among children in gifts and endowments. It is not permissible for a father to single out one of his sons with a gift to the exclusion of his other siblings, based on the hadith of Nu'man ibn Bashir: "Have you given all your children the like of what you gave him?" He said, "No." He said, "Then take it back." Equalization is achieved by giving the remaining children the same as what was given to the eldest child, or by revoking what was given to the eldest child. And whoever singles out some of them with a gift has sinned and is obligated to equalize. It is obligatory to honor one's parents and treat them kindly, even if they have wronged some of their children.