Can I relinquise my right to adopted child that was adopted in the mist of a divorce or do I have to pay childsupport

You adopted the child, which means you are the parent. You can't just relinquish your rights because this is not your biological child. You took on the rights of that child through adoption.

Unless someone else is asking to adopt the child, there's no way to get out of child support. You are, for all intents an purposes, the parent of this child, by choice no less.

You will have to pay support.

This is why it isn't easy to adopt a child. You signed off on the adoption. As soon as the court approved it, you became the child's parent just as if you gave birth to the child. This makes you responsible for supporting the child.