What is the ruling of Islamic law regarding a girl forcing a young man to commit zina with her, then demanding that he acknowledge the paternity of a child attributed to him?

The child born out of wedlock is not attributed to you, but rather to his mother, and it is not permissible for you, Islamically, to register him under your name. We advise you to continue your current marital life, and focus on building your family on religious foundations by raising your wife and children according to the Book of Allah and the Sunnah of His Messenger.