What is the ruling regarding a woman who discovered that her husband has a daughter from zina (fornication/adultery) before their marriage, and he refuses to acknowledge her, and what should she do with this husband?

You must live with your husband in kindness, and there is no justification for seeking a divorce. Your husband has repented of the alleged abomination, and "one who repents is like one who has no sin." The mentioned girl is not attributed to him. Therefore, you must turn a blind eye to this matter and do not spy on your husband, for that is forbidden. Have a good opinion of him and cooperate in obedience to Allah.