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How much does he earn?
How much does she earn?
Is either of them of them on public assistance?
Does the father of her child claim that child as a dependent?
Based upon the income of these two people neither of them has to pay any Federal taxes. If each files Single with each taking a child as a dependent.
Georgia does recognize 'common law' marriages as long as the union was established prior to 1/1/97.
If they have been together under GA law prior to that date then they may qualify for Married Filing Joint status. But I am not an attorney and I cannot speculate or give advise on this matter.
You should check with the State of Georgia to see if they qualify. If so then they could combine their income and dependents for Federal tax filing purposes.
Here is a starting point for you:
Unfortunately I know of no way you can get a tax break of any kind because the child does not live with you.