State tax filing

You didn't mention if you finally moved to SC during the year or simply continued to travel back and forth.

No, there isn't a minimum state tax amount you have to pay in GA. The amount of taxes you pay is based on your GA sourced income. If you owe GA income tax, it may be because:

• You didn't allocate your income correctly between GA and SC. See  How do I allocate (split) income for a part-year state return? 
• If you never lived in SC, file a nonresident income tax return BEFORE you complete your GA income tax return for accurate state income tax calculations. See How do I file a nonresident state return?
• You didn't claim a credit for taxes paid to other states, or
• You didn't have enough GA income taxes withheld from your paycheck for the amount of income you earned in GA.

Related information: 

• How do I file a part-year state return?