Another man is named as the child's father on the birth certificate,things diddnt work out for her and the man on the birth certificate,now she wants me to pay her child support,am I liable by law to do so even though I'm not on the birth certificate?

It depends on your state laws but generally-yes.

If you can be designated the legal father then you will be liable for support. Whether you can be named the legal father depends on local laws and other factors, like age of child etc.

If she goes to court for child support, you can demand a paternity test and may be able to challenge her petition on the grounds that there is already a legal father.

I would consult an attorney if and when she files for support.