1520s, native or inhabitant of Parthia (ancient kingdom northeast of Persia in western Asia), from Old Persian Parthava- "Parthian," dialectal variant of the stem Parsa-, source of Persia.
As an adjective, 1580s. Phrase Parthian shot is in reference to their horsemen, who were expert at racing forward, turning, and shooting arrows backward at the moment of retreat. The exact phrase is attested by 1832; the image itself was in use long before (for example Parthian fight, 1630s).
Or, like the Parthian, I shall flying fight ["Cymbeline," Act I, Scene VII]