Father has legal obligation to give support to his illegitimate child

Dear PAO,

I am a married man who had an affair with another woman. She gave birth to a child last year and she had been claiming that I am the father of her child. I did not sign the child’s birth certificate because I have doubts that I am the child’s father. Now the mother is threatening to file a petition against me for support. In this case, is there any legal obligation that I need to comply even if I did not sign the birth certificate? Can she force me to sign?