This page contains information regarding Star Trek: Picard, and thus may contain spoilers.
It was first introduced to the United Federation of Planets in 2266, when Balok, who enjoyed drinking tranya, served it to USS Enterprise personnel visiting a pilot ship sent from the Fesarius. (TOS: "The Corbomite Maneuver")
By the 24th century, tranya was available outside the First Federation. Odo ordered two "very cold" tranyas for Benjamin Sisko and himself at Quark's in 2371, while he was hosting Curzon Dax's personality during Jadzia Dax's zhian'tara. (DS9: "Facets")
Background information Edit
Tranya wasn't physically described in the script of "The Corbomite Maneuver". However, in the episode's final draft script, Balok said about the drink's name, "It is not easily translatable."
The tranya that Balok served the crew was, in fact, grapefruit juice, which young Clint Howard absolutely hated. He said in an interview that he had to work very hard at making it look like he actually liked it. (TOS Season 1 DVD special features)
In The Comedy Central Roast of William Shatner, it was implied that tranya could be an addictive beverage and that Balok had developed a bit of a drinking problem.