Alpha Centauri was an inhabited planet in the Alpha Centauri system. This system was located in the Alpha Quadrant.
In an alternate timeline, created by Jonathan Archer being infected by interspatial parasites, the Xindi destroyed Earth in 2154 and then proceeded to annihilate all other Human settlements, including Mars, Alpha Centauri, and Vega colony. (ENT: "Twilight")
In the mid-23rd century, in a cafe on this planet, the romance between Paul Stamets and Hugh Culber began. (DIS: "Magic to Make the Sanest Man Go Mad")
In 2338, Greta Vanderweg was born on this planet. (DS9: "Field of Fire")
This planet's quadrant of origin is inferred based on the position of its star system as seen in the star chart appearing in the Star Trek: Picard episode "Maps and Legends".
In the real world, a team of astronomers announced the discovery of Alpha Centauri Bb, an Earth-size terrestrial planet, in 2012. Three years later, however, another team of astronomers determined that this elusive ghost planet was all along nothing more than a measurement artefact. A second possible planet, known as Candidate 1, was detected in 2021 but has not yet been confirmed to exist.