What is the ruling regarding a Muslim woman remaining with her husband who claimed to be Muslim to marry her and then apostatized, knowing that she will lose her daughter if she separates from him?

If a man apostatizes from Islam, his marriage becomes null and void, and it is forbidden for him to cohabit with his wife, for at that point, they are no longer spouses but rather fornicators. If the woman is unaware of the impermissibility of this, then there is no sin upon her. The daughter is attributed to her father in lineage if he believes the marriage to be permissible, and she is considered Muslim, following her mother, if she is under the age of puberty, and her identity as Christian holds no weight. The unbelieving father has no right to her custody, and the mother must refer the matter to the Sharia court or Islamic centers. One must be wary of rushing into marriage with someone who merely feigns Islam.