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The credit will be applied first. So, if you know you are going to have a credit (i.e. you just had a child) that will eliminate your tax liability, you could lower your withholding.
See IRS Pub 505, page 53 - "You do not owe a penalty if the total tax shown on your return minus the amount you paid through withholding (including excess social security and tier 1 railroad retirement (RRTA) tax withholding) is less than $1,000"
Any tax credits are going to reduce your tax liability first and then that number will be used as the total tax shown on your return.
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