S.C. Code Ann. § 7-13-190
(B) In partisan elections, whether seeking nomination by political party primary or political party convention, filing by these candidates shall open for the office at twelve o'clock noon on the third Friday after the vacancy occurs for a period to close ten days later at twelve o'clock noon. If seeking nomination by petition, the petitions must be submitted not later than twelve o'clock noon, sixty days prior to the election. Verification of these petitions must be made not later than twelve o'clock noon forty-five days prior to the election. If seeking nomination by political party primary or political party convention, filing with the appropriate official is the same as provided in Section 7-11-15 and if seeking nomination by petition, filing with the appropriate official is the same as provided in Section 7-11-70.
A primary must be held on the eleventh Tuesday after the vacancy occurs. A runoff primary must be held on the thirteenth Tuesday after the vacancy occurs. The special election must be on the eighteenth Tuesday after the vacancy occurs. If the eighteenth Tuesday after the vacancy occurs is no more than sixty days prior to the general election, the special election shall be held on the same day as the general election. If the filing period closes on a state holiday, then filing must be held open through the succeeding weekday. If the date for an election falls on a state holiday, it must be set for the next succeeding Tuesday. For purposes of this section, state holiday does not mean the general election day.