First, with no background about your stepson’s life, history with dad, or relationship with you, I have no idea what is behind his silence. There could be an infinite number of contributors. Does he struggle with depression or anxiety? What happened with his birth mother? Is there trauma associated with that? Could his silence be related to feelings of inadequacy or fear in his relationship with his father? Does he have developmental or autism spectrum-related challenges? Is he naturally shy?
With all that said, let me share a few principles that you can consider as you try to have a positive influence. I will base my advice on two things you said in your brief question: He is “stubborn” and “refuses to speak with his father.” And “What can I say to him so he’ll open up?”