For the father on the birth certificate not to be the biological father, either the mother or him, or both, committed a crime. It is a crime to falsely swear on a birth certificate.
There is NO such thing as a father "giving up rights." Rights belong to the child and a =man cannot sign those away - with one exception - if he gives up a child to someone who is adopting the child.
Although you left out almost every fact that matters, including why you perpetrated a criminal fraud, if a child was born to a married couple, the husband IS legally the father. There is one exception. If paternity is disproved in the divorce, then a judge could enter an order that the child was not the husband's. This is unlikely to happen unless the real bio-dad steps up to the plate at the time, as the law does not favor making a legitimate child illegitimate. In other words, even with a DNA test to the contrary, the legal father is the husband in most cases.
Given the complexity of this situation, retain experienced counsel. Any chance of fixing things depends on why the fraud was committed, and on whether bio-dad can be found and will cooperate.
