There is no credit that is for a foster child, unless the foster child qualifies as your dependent. If the child is your dependent, you may be able to claim the same credits you would be eligible to claim for a biological or adopted child.
Please go to the link below for information about the Child Tax Credit:
https://turbotax.intuit.com/tax-tools/tax-tips/Family/7-Requirements-for-the-Child-Tax-Credit/INF156...
Even if you can’t claim your foster child as a dependent, you may be able to deduct unreimbursed expenses (expenses in excess of the foster care payments you receive.)