Beta Geminorum, also known as Pollux, was the primary of the Beta Geminorum system, in the Alpha Quadrant.
In 2256, this star's location was labeled on the star chart "Alpha/Beta Quadrant Overview" in the ready room aboard the USS Discovery. (DIS: "Magic to Make the Sanest Man Go Mad")
In 2257, during the first Federation-Klingon War, this star's system was occupied by the Klingons. (DIS: "The War Without, The War Within")
In 2293, the location of Beta Geminorum in the Milky Way Galaxy was labeled in a star chart that was in Captain James T. Kirk's quarters aboard the USS Enterprise-A. (Star Trek VI: The Undiscovered Country, okudagram)
In 2399, the location of Pollux was labeled in a star chart that was in Fleet Admiral Kirsten Clancy's office at Starfleet Headquarters. This star was in or near to Federation space. (PIC: "Maps and Legends")
This star was only mentioned in writing.
In The Explored Galaxy, Beta Geminorum and Pollux were depicted as two distinct stars, even though they were established to be synonymous in "Who Mourns for Adonais?".