I have a similar situation, but i signed the birth certificate, and they tried to get me for child support, after it was all done with, my name was never taken off the certificate, and my payment was set at zero,the mother can name the child what ever she so please, as long as you don't sign the birth certificate the Court's can't do anything, but if you sign the certificate, he's your responsibility, there for she can get you for child support,if you do sign the certificate, file for 50/50 custduy.
If you put your name on a kid that's not yours then that's a form of acknowledged paternity and you can be cited for support fees until DNA is established. Lol don't do it.
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