Is it permissible for the son to own a house registered in his name, even though its registration was by mistake and not intended as a gift, and the house was built with the money of the deceased father and is inhabited by the mother and sister?

It is not permissible to seize a house that was mistakenly registered in your name, as it is an inheritance to be divided among the heirs according to their legal shares. You must fear Allah and not take what is not rightfully yours. Who will save you from accountability on the Day of Resurrection when rights are restored to their owners through good and bad deeds? The wise person is he who leaves the injustices of people so that he may come lightly burdened on the Day of Resurrection.