It showed SC was issuing an additional $4000 something for anyone with a child under six. At the end its not showing in my refund?

Yes, there's a deduction, not a refundable credit, but it may lower your tax liability or amount due, and it could increase your refund based on state taxes paid/due.

-Child deductions: South Carolina offers a deduction of $4,300 for each dependent child and an additional deduction of $4,300* for each child under 6 years of age.
More than 727,000 returns for 2020 claimed dependent deductions, and 246,094 returns claimed exemptions for children under age 6.

This is a deduction of your income which will lower your tax liability. Not refundable but deducts from your qualified SC taxable income.

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