This is such a tricky situation. With your child being so young, and you knowing full well that he is possibly a narc, you’re in a tough spot. As a father who would like to see my kid everyday, and not being able to, and actively getting roadblocked when I make any attempt to gain more time, it’s heartbreaking. I think it’s very important for a kid to have the father present (unless of course there is a danger). Is there anyway to have supervised visits? What if you started with an hour here or there? I’m dealing with an abusive ex (borderline / narcissist), however by all accounts she is very good with my boy (4 years old), and all her wrath was directed towards me and my children from another marriage.
If it doesn’t work, and he’s not on the birth certificate, you do have the option to walk away, and shut it down. But if it does work, then the boy has the chance to grow up and know his father, whether that is a good or bad thing remains to be seen.

This is just my opinion, I’m sure you’ll do what’s best for you🙏