Ok so my daughter will be 3 this month and I have been the one solely supporting her now here's the sticky situation I was pregnant by another man and my ex and I had gotten back together knowing she wasn't his biological daughter he signed her birth certificate to take on any parental responsibility however he never did I've asked him several times to relinquish his rights as he has another child on the way and I feel as though it would be better for everyone that he just sign over his rights what is the easiest and most efficient way to get this done so we can all move on with our lives?

Really bad situation, he cannot just relinquish his rights, he will have to challenge paternity ( if he even can now depending on the state law) or the real bio father will have to challenge paternity. You may be stuck with him as the father.
Perhaps if you filed for child support, he would decide to challenge it.

Of course there is the entire issue of fraud for signing that he was the father, but judges do not often have criminal charges filed.

He and I are both aware that he is not my daughters biological father even when he signed her birth certificate is this enough for him to relinquish his parental rights? He hasn't supported her since she was born he simply signed the birth certificate because I was in a violent relationship with the biological father and we thought it would be in her best interest for him to act as her father. Now he has another child on the way with his girlfriend and I think its best for the both of us as well as my daughter for him to relinquish his rights what the best way to go about this when he has no interest in being in her life?

Where did you even get the idea he can relinquish his rights? There seems to be a myth that a parent can just sign a paper and relieve themselves of the responsibility of a child. This is nothing more than a myth. Once he signed the birth certificate and acknowledged paternity he became the child's legal father. Even though he did it fraudulently.

The only way his rights will be terminated is if a court of law does it. And, depending on local laws (ANY question on law needs to include your general locale as laws vary by area. ) it may even be too late to take this to court.

P.S. to add follow-up, please use the Answer box below, not ask a new question.

The fact that both you and him KNEW that he wasn't the father when he signed the birth certificate removes any challenge he would have to paternity. Usually a paternity acknowledgment can only be challenged if the father can prove that he was deceived into believing that he was the father when the mother knew that he was not the father. You have stated that this is not the case.
Furthermore, a judge may be very reluctant to leave you child legally fatherless when the two of you knowingly put false information on the paternity acknowledgment. As Fr. Chuck mentioned, unless you can locate the biological father to challenge paternity, you may be stuck.