What is the correct course of action regarding an illegitimate child of a non-Muslim woman who refuses abortion or abandonment, given the father's desire to raise the child in an Islamic environment, and his fears concerning the mother?

You must be wary of adultery and its preludes. What is obligatory is to embrace righteousness and adopt the means that aid in steadfastness upon it. This child, born of adultery, is not attributed to you; rather, he is attributed to his mother, and she is legally responsible for him.