I think you may be referring to an earned income credit and a child tax credit. For the earned income credit, you have to have earned income, which would be income from a job or net self-employment income. You mention $1,000 in income, if that is not earned income you would not qualify for an earned income credit based on what you mention here.
For the child tax credit, you would have to have over $2,500 in income to qualify for an additional child tax credit. You don't qualify for the normal child tax credit since you don't have any income tax.