refused to put my name on the birth certificate

(las vegas, nv )

My ex told me she couldn't get pregnant because she was raped as a child. After my ex found out she was pregnant she broke up with me and stopped talking to me (and kept the ring). Now my son is 5 yrs of age , and she did the same thing to another man but said she was on birth control. Now she has two children and is filing for child support. She refuses to let me see him, and moves all the time so i can never get a hold of her.

What should I do ? am i going to get 5 yrs of back pay?
Can I fight her for not paying the back pay? I have a child with my wife with special needs and im afraid im not going to be able to afford to support my family.

I know it looks bad I didn't take her to court but how do you fight for a kid you have no proof hes really yours,Or even have doubts yourself. I always treated him like my son but had doubts in the back of my mind. I love him and would love him to live with us , but from what ive read is its going to just look bad that were trying to get custody after we've been served with child support.

Do you think I can still get him for holidays and summers? We live in different states so i can't just have him for a weekend.