Is the child of adultery considered a mahram to the wife and children of the biological father, and is it permissible to consider him a member of the family?

Repentance and guidance are the greatest blessings Allah bestows upon His servant. As for children born out of wedlock, if the woman who committed adultery was married, the child is attributed to the husband, unless the husband disavows him through mula'ana (oath of condemnation), in which case the child is attributed to his mother. If the woman who committed adultery was unmarried, the correct view is that the child is not attributed to the fornicator; rather, he is attributed to his mother, and the fornicator does not inherit from him. As for mahramiyya (prohibition of marriage), the prohibition of marriage does not necessitate the mahramiyya that permits khalwa (private seclusion). Rather, mahramiyya remains confined to the legal mahram relatives.