Is a woman lawfully married permitted to claim that her child is not her husband's and demand maintenance and rights for the child from another man, while she is still married to her husband? And what is the lawful solution to this issue?

It is impermissible for a wife to attribute her son to anyone other than her husband, for the son is attributed to the owner of the bed (i.e., the husband). She must fear Allah and conceal herself, as publicizing disobedience is among the destructive sins, for the Prophet, peace and blessings be upon him, said: "All of my Ummah are safe except those who publicize [their sins]." By her action, she harms herself, her son, her husband, and her family. She must cease this act, for it is not permissible in Islamic law.