You can request termination of any accruing child support payments for your "former child" that you gave up for adoption and which was adopted by filing a petition with the court where the child support order lies. The problem lies with trying to eliminate accrued pre-adoption arrears.Under the laws of all states in this country since the child was yours pre-adoption, you are obligated for all accrued and unpaid child support obligation amounts prior to the adoption of this child.