It depends. Generally, the amount of Child Tax Credit (CTC) depends on the dependent ages and your income. As Critter-3 states, the Child Tax Credit is non-refundable and with an income of $10,500 you likely owed zero tax on form 1040 line 16 and therefore zero CTC will apply (line 19). However since you had over $2500 of earned income you would be eligible for the Additional Child Tax Credit (ACTC) which is refundable (line 28). That ACTC will generally be 15% of your earned income over $2500 up to $1600 per child. You stated your income was around $10,500. Using that as an example, the amount over $2500 is $8000 x 15% = $1200 of ACTC.
Here are some links with more helpful information.
TurboTax article Additional Child Tax Credit
TurboTax article Child Tax Credit
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