Let's clarify which tax year you are asking about. For tax year 2022, you are not eligible for any sort of child-related credits or income tax refund unless you worked and earned taxable income; then you could be eligible for earned income credit and perhaps the child tax credit for children under the age of 17.
For tax year 2021 if you can claim your children as dependents you may be eligible for the child tax credit and the recovery rebate credit for the qualifying children that you claim as dependents. Those credits are available even to a parent who did not earn any income--but only for 2021.
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