Jadzia Dax was the persona adopted by a non-corporeal entity who traveled from the Gamma Quadrant through the Bajoran wormhole and had taken a position in the plasma fields near the Denorios belt, where they read as elevated thoron emissions in 2369.
That year, this Jadzia Dax persona created by the imagination of Julian Bashir. As she hung all over Julian, he nervously tried to play off the awkwardness of the situation. When Dax requested they go to his quarters, he told her he didn't have time for this, and she disappeared.
When the real Dax questioned Bashir about the submissive personality of her doppelganger, the Dax entity returned and protested the implication, responding, "I'm just not the cold fish you are," adding "If you'd get down off your high horse, you'd start to appreciate Julian." As she attempted to entice Bashir to "Stop denying all those yearnings you feel [or] you'll never know what you missed."
She, along with two other's in the imagined personas of Buck Bokai and Rumpelstiltskin, later converged in the replimat to discuss their findings, only to be confused by the irony of their results. Dax claiming, "Why would mine create a woman and then reject her?"
Following the crew's realization that their own imaginations were responsible for the events that transpired on the station, the crew was finally able to return things back to normal. After returning to his office, Bokai revealed himself to Benjamin Sisko, explaining their actions, stating that they were "on an extended mission exploring the galaxy. Awhile back, we followed one of your ships through that "hole in space" out there. We've been watching you, trying to figure out the rules of your game." (DS9: "If Wishes Were Horses")
This alien portrayal of Jadzia Dax was played by Terry Farrell.
She was identified as "Dax" in the script, until the "real" Dax appeared, then the script notes stated, "The fake Dax hereafter known as "Dax #2"."