First, you can't sign your rights over. Only a court can terminate parental rights and courts are very reluctant to do so. There is a sticky note at the top of this forum that discusses this issue.
Second, we need more info here. How did you find out the child is yours? Was she married when the child was born? You say she let another man think he was the father besides the husband? Where has this happened?
Right now, unless a court has named you the child's legal father you have no rights nor responsibilities towards this child. If you want to be a part of this child's life then you will have to first go to court to establish paternity. Depending on where you are (ANY question about law needs to include a general locale as laws vary by area.) the window of opportunity to establish paternity may have passed.
Once you have established paternity, you petition the court to allow visitation. This can be done as part of the same case. Most likely the mother will then petition the court for child support from you.
I would strongly advise hiring an attorney to help you through this.
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