You can not buy children, that is illegal, so if you had a deal to buy a child you are adopting, I doubt the adoption would be legal for one, but no one can inforce the payment for the sell of a chaild.
Now if you mean you are getting a divorce, and have an adopted child, yes, you will pay child support just like it is your own child ( because legally they are)
If you mean you are the birth mother and father, and a child is adopted, then no you do not pay for their support after they are adopted.
Your question could mean many things, not sure exactly which you are talking about
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