Much depends on the timing of the conception and birth of this child in relation to any marriage to your ex. Also, it is possible that a court order was entered without proper notice to you. In order to get accurate answers to your questions, you should obtain a copy of the court order under which the child support is apparently ordered. Then you should retain legal assistance to analyze whether it was properly entered and can be set aside. If a paternity order was properly entered, you certain can file a related petition under the same case number to have your parental rights decreed. Whether DNA testing will be court-ordered at this late date is uncertain, and in order to proceed with DNA testing at your own expense, you will likely need a court order to compel the cooperation of the mother and child.
Best wishes for an outcome you can accept, and please remember to designate a best answer.
This answer is offered as a public service for general information only and may not be relied upon as legal advice.