Am I entitled to deny my son's paternity, remove my name from his birth certificate, and divorce my wife, after being informed by the doctor that I am sterile and unable to have children?

The basic principle is the innocence of the wife, so it is not permissible for you to harbor ill suspicions about her, based on the Almighty's saying: "O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin." (Quran 49:12), and the Prophet’s (peace be upon him) saying: "Beware of suspicion, for suspicion is the falsest of speech."

You should not divorce her merely based on suspicion, as divorce without need is disliked, and some scholars may even deem it forbidden in this situation.

Regarding paternity, Islamic law takes great precaution, and the basic principle is that "the child belongs to the bed." So, if you have a wife and she gives birth to a child, that child is attributed to your lineage if it is possible. This fundamental principle should not be abandoned based on the statement of a doctor who may err. If paternity is established, it is not permissible to deny it.