In addition to the great information provided by, xmasbaby0, you may have qualified for some of New York's refundable credits. If you are claiming your child or children as dependents you may qualify for the Earned Income Credit, Dependent Care Credit, Child Tax Credit, and others. Refundable credits can get you a refund even when you do not owe any taxes. Things You Should Know About Refundable Credits
Refundable tax credits are called “refundable” because if you qualify for a refundable credit and the amount of the credit is larger than the tax you owe, you will receive a refund for the difference.
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