I think this situation is actually fairly common and far more common than anyone realises. I know two families with the same issue.
In one case, the father knew about the child but had no contact and had never mentioned it; when the child was mid 30s, they literally turned up on the doorstep. The father had been married to his wife for +30years and they had children of a same age. Once the initial shock and trauma had passed, they all developed a good relationship. Sorry to say, call me cynical, It was probably helped by the fact that the child was a bit of a star - think Bill Gates style.
In the other, the father knew and had sporadic contact. Again the disclosure of it was when the child was an adult.
I wouldn't necessarily jump up onto the "he's a liar and you must leave him." for this. It wasn't his choice to have a child and it's not really that surprising that he'd lie about it. It's obviously terrible to lie to you but completely understandable. And I don't subscribe to the "if he lied about that then what else is he lying about" argument either. This is a very specific and compartmentalised issue.
The real question for you is how you feel about it long term. Do you love him? Want to stay with him? Can you live with this? If you can and you do, then try to accept it and move on. But you have to draw a line under it otherwise it will be something you return to again and again in arguments and it will undermine any possible future relationship you have.
He said he won't see him again if I don't want him to. I haven't responded to that.
Cecil Parkinson and Sara Keays is what I say to that. He agreed to something similar and history has judged him very harshly.
It's up to you what you can live with. If your view is that is what you need to get through it, then that's your call. I wouldn't judge you - but as set out on here many people would do.