I had been with the same man for many years. I got pregnant he left. He moved to another state and is taking care of his girlfriends kids. I begged him to be here for the birth of my sons {i had twins} He wasn't. One of my sons got sick and has had two open heart surgeries. I have begged him to be apart of my babies life he has not I have begged him for help financially he won't give me any. I haven't taken him to court At this point in my babies life I just don't even want him around my son has had 4 serious surgeries since his birth. They are only four months old . I am scared he's going to decide later on in life he wants to be around, that's not fare to me or my boys Legally what are his rights

You drag his buttt to court, if he name is on the birth certificate he has full rights already, if not, all he ever has to do is just go to court and prove DNA, so that fact is just a fact. What you should have done a day after they were born, was file for full custody and child support.

So since you have not done anything, you are not restricting any of his rights esp if he is on the birth certificate, Get an attorney and start doing things legally.

Fr. Chuck is right, at least get the custody and the child support done. Your kids are entitled to be supported by the father, at least financially. He has rights, but he has to go to court himself to enforce anything, even visitation. Until then, the ball is yours to run with, and I urge you to start NOW!!