We have a foster baby and we receive money from the state. Does the money from the state qualify as her paying half of her support? What about would be half?

No, your child is not paying for half of her own support.   Foster care payments by the state are considered as expenses paid by the state, not by the child (this is good news for your tax return).  If the baby lived with you for more than 6 months under an order of foster care (if born after July of 2016, then she lived with you the remainder of the year), she would still be claimed as a qualifying child.  This means that you can claim Child Tax Credit, Additional Child Tax Credit, and Earned Income Credit for this child if you meet the other requirements.  Here is a useful FAQ that gives more information:  https://ttlc.intuit.com/replies/4835245