The child tax credit can only reduce your tax liability to zero. If you only have $500 income you have no tax liability to reduce. In fact you do not even need to file a tax return. If single and one child dependent you would have to have at least $14,100 of income to have any tax liability for the credit, or more than $3,000 income for any additional child tax credit.
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**