How can a father who believes a baby isn’t his get a paternity test and name extracted from the birth certificate?

Short answer based upon the facts provided in your question, the paternity for the minor child has most likely not been established and no obligations would fall upon you, but the way the courts are in Louisiana you should bring a disavowal action to determine whether or not you are the father of the child. Since the Louisiana legislature amended the family law portions of the civil code in 2016, signing of the birth certificate no longer establishes legal paternity. If you and your ex never married, the only way those parental rights and obligations would fall to you is if you had executed an act of acknowledgement of paternity of the minor child. In a perfect world where the application of the statutes were strictly applied, you wouldn’t have to go to court to contest paternity and possible child support. Yet, this is not a perfect world, any person can file anything in a court to have it heard, and your ex may bring an action to establish child support even though paternity has not been established. In such a case you would be forced to not only contest the establishment of child support, but to also contest the paternity. All that said your issue can be resolved. It will require what is called a "disavowal action" and, if she is unwilling to submit the child to a DNA test, a court will order it. Under Louisiana Civil Code Article 187, you may disavow paternity of the child by a showing of clear and convincing evidence that you are not the father. Testimony alone will not be sufficient and will need to be corroborated by other evidence, like a DNA test. Under article 189, the action for disavowal of paternity must be brought within one year from the day of the birth of the child, or the day the you knew or should have known that you may not be the biological father of the child, whichever occurs later. During the disavowal action you may request and the court will order a DNA paternity test to be taken.   If this is something you are interested in pursuing please feel free to set up a free consultation with my office and I would be more than happy to help.