What is the ruling of the Sharia and the worldly law regarding a wife who has been cheating on her husband for 10 years and has a child from her betrayer, knowing that the husband has discovered the matter and is trying to catch them in the act?

If you become certain of your wife's relationship with a foreign man, you must first try to sever this relationship with wisdom. If she does not respond, she is treated as a rebellious wife (nashiz). If she persists and you are unable to prevent her, we advise you to divorce her, because someone like her cannot be trusted with honor, and remaining with her is an affirmation of evil, which is cuckoldry (diyatat).

As for your statement that the child is from him, this is a grave assertion. The general rule is that a child born on your bed is attributed to you. It is not permissible for you to disavow him unless you are certain that he is not yours, and in that case, it must be through li'an (oath of calumny). It should be noted that disavowal must occur immediately after the birth or upon learning of it. Anyone who remains silent without excuse does not have the right to disavow. Therefore, you must refrain from making such a statement.