Can a father sign away his rights to the mohter in the state of Nebraska? He don't want to pay and I don't want him to have visitation rights!

Yes a father can sign away his rights if he choose to do so he has to go to court

Please refer to this thread: https://www.askmehelpdesk.com/family-law/signing-over-rights-read-first-116098.html

Only a court can issue a TPR. And courts are very reluctant to do so. They will never do so to allow a parent out of paying support.

Unless the parent is a danger, then they have the right to be a part of their child's life.

Well, guess what?

*I* don't want to pay for your child, and I don't want your child growing up without a father figure.

I'm a taxpayer.

You guys liked each other enough to have sex. Figure out how to be nice enough to each other to raise your child---because NO COURT is going to terminate his parental rights so that you can forget you had sex with him and he can get out of taking responsibility for his child.