Me and the mother of our 3mnth old have agreed to not seek child support if I sign over my rights, what do we need to do to make it legal

There is this myth that a parent can just sign over their rights. But it is only a myth. Not going to happen.

Only a court can terminate parental rights and they will only do so under limited circumstances. You will NOT be allowed to relinquish rights to get out of child support.

The mother doesn't have to pursue support and you don't have to be a parent. But if the mother applies for public assistance the state will want to go after you for support.

Both of you move to some nation that may allow it. If you are in the US, this is not going happen. You can both "agree" and just do it, but it is not legal. First unless she has someone else ( married) and they will adopt, you can not just sign over your rights.

Next you can not sign over collection of child support, an example in the US if she or the child collects any welfare the state will come after you for repayment and/or child support.

So forget it.