S-C (sometimes EX-SC during the Republic) stands for [ex] Senātus Consultō "by decree of the Senate." It indicates that the Senate ordered and guaranteed the coin. After Augustus, it indicates that it was minted somewhere where the Senate had nominal control (ie not an "Imperial" province), though I think this distinction breaks down later on in the Empire. For instance, your coin from Antioch was in Syria, an Imperial province. S-C is most common on "base" coins (ie not gold or silver), but sometimes appears on those as well.

During the Republic, the EX-SC legend indicated that there was a minting of coinage beyond what was usual by the three money guys, the tresvirī monētālēs (hence the need for a consultum to get it done, and probably at the behest of a quaestor, praetor, or consul).