I qualified for federal child tax credit, why would I not qualify for the local State Child Tax credit. She does not live with me but I pay $856 a month in child support.

Which state?

 

Child support does not count in general for anything when it comes to claiming a child on taxes or any type of deduction or credit.  

 

For federal, your child support does not allow you to claim the child, however rules under divorced and separated parents allow you to claim the child tax credit if the custodial parent agrees to let you claim the child.

 

State rules vary and may or may not conform to federal rules.