I have been married for 14 years and I just found out by mere accident that my husband has a child outside of our marriage, only because he accidentally called my phone while he was spending time with the child. The child is about 3 or 4 years old. I only know because she called him daddy a 100 times and he responded as a father should. Of course he had a lame story and denied it, so I know he will not be honest with me. I have the phone call recorded for my own records. The problem I'm having is, I don't know the women or child's name. I need to know if he signed the birth certificate. How do I go about finding that information out.

You may hire a PI, or you could ask him, If going though divorce court you require him to supply this information as part of your inquiry.

If he did not sign the birth certificate there is no "evidence" to find. You will need to contact your states ( if in the US) department of records, and can search normally by parents name if listed on birth certificate.