The Taugan system was a planetary system. This system was located in Sector 2158, a region of space in the Beta Quadrant.

Several of these planets had been raided by the mercenaries led by Arctus Baran in 2369 and 2370 in search for ancient Vulcan artifacts. This was mentioned in a conversation between Commander Riker and Vulcan minister Satok. (TNG: "Gambit, Part II")

This star system was only mentioned in dialogue.
This system's quadrant of origin is inferred based on the position of neighboring systems, such as the Calder system and the Draken system, as seen in the star charts appearing in the Star Trek: Discovery episode "The War Without, The War Within" and the Star Trek: Picard episode "Maps and Legends".
In the script, Riker say Taugan sector instead of system. A Taugan sector appears in the Star Trek: Star Charts (p. 66), containing a star named Taugus (Gamma Equulei) and one called Barradas, presumably associated with the planet Barradas III from the episode.
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