If I live in Georgia and I file my taxes as married but filling separate and I made 11,293.93 and I'm claiming one dependent how much would my federal taxes be. If I had Federal income taxes withheld which was 1010.64. And state was 614.30.

Is the dependent a child or an adult? Is the adult disabled? This is important because you may be eligible for the Earned Income Credit.

As it stands, with no EIC, you will get ALL of your withheld federal income taxes back, because the combination of your standard deduction ($5,150) and two personal exemptions (yours and your dependents) ($3,300 x 2) totals to $11,750, which exceed the income you cited. You would owe ZERO federal income taxes.

My dependent is my child so how much would I get back on my refund.

Your refund is $3,758, $2,747 of which is the Earned income Credit.

Your GA refund is $563.