Is an alleged father of a 46 year old child legally responsible for anything for this adult child?

Scenario: A 46 year old adult posts message on Facebook that she is your child. You have never been contacted in 46 years, do not believe this is your child, was never told by the mother that she was your child, and your name is NOT listed on the birth certificate. What, if, any, legal action can be taken towards you at this time? What is the Statute of Limitations in this type of case? Are there any denial of paternity forms that should be filed by male? Can this adult child get a court order for DNA testing to prove paternity? - thank you