No. You will not have to file any returns for your son if his total income from everywhere is $2,600.
Normally you would file a nonresident South Carolina return and a resident New York return. Going to college is considered a temporary absence, so your son is still a New York resident.
However, SC doesn't require you to file if you are not required to file a federal return and the NY standard deduction for single filers is $3,100 so there is no NY income.
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