I owe back child support for my other children, I did however have a new baby, will child support take the credits given to my new baby?

[xmasbaby0]

If there is an offset order on record with the IRS and state, yes, your refund will be seized for the back child support.  

 refund offset.

https://www.irs.gov/uac/tax-refund-offsets-pay-unpaid-debts

 IRS Treasury Offset Program Call Center at 1-800-304-3107

 https://www.irs.gov/uac/tax-refund-offsets-pay-unpaid-debts

https://ttlc.intuit.com/community/refunds/help/what-is-a-refund-offset/00/26301

Reduced Refund      https://www.irs.gov/taxtopics/tc203

 NOTE: You can contact the IRS Treasury Offset Program Call Center at 1-800-304-3107 to ask if they have an offset for you on file. TurboTax would not have that information.

https://turbotax.intuit.com/tax-tips/tax-payments/who-can-garnish-an-income-tax-refund/L7cPPzDyc

[Opus 17]

if you owe a debt that is eligible to be recovered by offsetting your tax return, then it can be offset.  Having a new child which increases your tax refund, does not protect the refund from being offset for prior debts.