You mention the $500 child tax credit, so I assume your child is 17 years old or over. He would have to be under 24 years old and unless he was a full-time student, would have to have earned less than $4,400 to qualify as an "Other Dependent."
You need to make sure you didn't indicate in TurboTax that his father was claiming him as his dependent. Also, you need to indicate that you provided over half of the child's support and he lived with you for over half the year.
If the child's father claimed him as his dependent, you will need to mail your tax return in and the IRS will straighten that matter out down the road.
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