How does the law work in this case?

by chris
(missouri)

First off I live in Missouri. My wife and I married three years ago in Feb. She has two children of her own, which are with the father in Tenn. She really has no rights, I believe it is a non-visitation deal. She has a lump on her child support. Now, my question is, do I ever become responsible for that support? I mean is there anytime to where they can garnish my pay for children to whom I have never met or have any relationship with?