Sun worship was a type of (usually primitive) religion, centering on the worship of the sun.
The Roman Empire on Earth had no sun worshipers. Upon finding the seemingly sun worshiping Children of the Son on 892-IV, a planet with a civilization closely paralleling Rome, Leonard McCoy showed surprise at this striking difference. Spock furthermore thought it illogical for such a religion to develop a philosophy of total brotherhood, as appeared to have happened. However, the inhabitants of 892-IV did not turn out to worship the sun after all, but "the Son" of God. (TOS: "Bread and Circuses")
The Roman Empire did in fact have a sun god, Sol Invictus.