I suspect you did not actually "sign the birth certificate" at the birth of the child but, rather, signed a "voluntary acknowledgment of paternity" that resulted in your name being listed as "father" on the birth cerificate issued but the state's Vital Records agency.
By mandate of federal law, 42 USC § 666 (a)(5)(D)(iii), each state is required to have in place procedures allowing for a signed voluntary acknowledgment of paternity to be challenged in court on the basis of "fraud, duress, or material mistake of fact" if the acknowledgment was signed without parentage testing having been done. The party making the challenge has the burden of proof on the issue of fraud, duress, or material mistake of fact.
Keep in mind, however, that some states impose time limitations (one year, two years, etc.) for bringing the challenge. Other states (Oregon, for example) allow such a challenge to be made "at any time." So check with the laws of the state that would have jurisdictional authority over the mother (as she would be the respondent in the case).
If the challenge is successful, your name will be removed from the child's birth certificate even though without the consent of the mother.

