Persia was an ancient Earth region and empire, ruled by the Persians, that was located in south-western Asia, and existed during the mid-1st millennium BC.
In 2267, Trelane claimed to possess battle flags and pennants from "the hordes of Persia" among others. (TOS: "The Squire of Gothos")
As he mentioned Persia along with the Grecian war galleys, he might have referred to the time when Persia fought against Greece in the 5th century BC.
Persia invaded Greece in 480 BC, engaging the Spartans, led by King Leonidas, at the Battle of Thermopylae. (DS9: "What You Leave Behind")