Is the father, who has no authority over his son, legally obligated to provide for him, when the mother has raised the son to believe that her husband is his father and prevents the biological father from seeing him?

It is not permissible for the mother, grandmother, or anyone else to prevent the father from visiting his son, inquiring about his well-being, and taking care of him. The son needs his father's teaching and discipline, and to be entrusted to someone who will teach him the Qur'an, writing, and crafts. As for the child's maintenance, it is obligatory upon the father as long as the child is in need of it, and it is not waived if the mother prevents him from visiting his son.