So I finally adopted my friends daughter that I have taken care of for 13 years... Well her biological father owed back child support and is now out of prison and has a job.. So the attorney general started taking out of his checks the money that was owed... Shouldn't the child receive that money??

Who is receiving that money?

No, the child has no rights to back child support.

Nope, the back support is owed to the parent at the time. When the adoption was final any further support obligation ended.