The mother of my 13 year old daughter wants me to continue to pay her child support to have custody of my child... is this against the law?

What do you mean by continue to pay? Child support and visitation are 2 different things. They are not connected in the eyes of the law.

Is there a visitation order in place? Are you up to date on your child support? Is there a support order in place?

Do you mean she will give you physical custody if you pay her ?

Your question is not too clear, some more information would help.