What is the ruling on living with a woman and having a child with her without a legitimate marriage, and is the child attributed to his father in this case?

If the wife gives birth before six months have passed from the date of marriage, the child is a child of fornication, and his lineage is not established from the husband. However, if the birth occurs after the aforementioned period, he is the husband's child and is attributed to him, and he has rights over him such as maintenance, breastfeeding wages, and upbringing. As for living with the woman who separated from your brother, it is not permissible if it leads to khalwah (private seclusion) with her and looking at her, because she is a non-mahram (definition).