Airponics

From Memory Alpha, the free Star Trek reference

Airponics is the cultivation of plants without soil, by suspending them in an oxygen-rich environment and misting their roots with nutrient solution.

The Kantare created an airponics room aboard their stranded ship. It was discovered by Commander Tucker and Subcommander T'Pol when they've followed a shadow. In this airponics room, Tucker first met Liana. Later, Liana offered Tucker a fruit from their airponics, the lorella. (ENT: "Oasis")

Kes established an airponics bay on USS Voyager, along with a hydroponics bay. (VOY: "Elogium", "Cold Fire")

In 2372, the yields from Voyager's hydroponics lab were coming out low. (VOY: "Deadlock")

In 2375 Ensign Doug Bronowski worked in Voyager's airponics bay. (VOY: "Someone to Watch Over Me")

The vegetables in the airponics bay were beamed off the ship when Voyager entered The Void in 2377. (VOY: "The Void")

[edit] Background

The accepted term for the method is aeroponics. However, airponics is the term used in the series. Aeroponics is a very real technology developed in the 20th century.