You don't need your spouse to sign any papers in order to get your divorced finalized. You begin by filing a Complaint for Dissolution of Marriage and have him legally served through the Sheriff's Department. If he fails to respond you can go into court and get a default entry of divorce. You probably need an attorney to make sure you complete all of the steps.
If he is not the biological parent of your child, but the child was born during your marriage, you would need to institute a paternity case against the true father. It is not clear if you have a paternity, custody and support order or not, you just say "agreement", but I'm not sure what that is. I'm not sure how, if your husband is not the child's biological parent and the child wasn't born during the marriage, how his name can appear on the child's birth certificate. If the child already has a father through a paternity case, your husband is excluded from claiming this child.
All in all, it sounds like you have a really serious case with significant issues. It would be best to hire an attorney to resolve these for you. I offer a free consultation if you would like to meet. See my links. Good luck.
This should not be considered legal advice, but rather simple information. You should consult a lawyer to review your unique situation. No client-lawyer relationship exists until you sign something indicating there is.
Have him served and then follow-up with getting the court to order the matter finalized. The custody agreement should be filed, since any children born during a marriage are presumed to be the married couples. Get a lawyer and have them take the steps necessary.
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