Multiple realities
(covers information from several alternate timelines)
Beta Simmons was a star system in the Alpha or Beta Quadrant.
In 2367, Beta Simmons' position was labeled on a tactical situation monitor in Captain Benjamin Maxwell's ready room on the USS Phoenix. (TNG: "The Wounded", okudagram)
In 2366, in an alternate timeline, during the Federation-Klingon War, Beta Simmons' position was labeled on a tactical situation monitor on the bridge and in the ready room of the USS Enterprise-D. (TNG: "Yesterday's Enterprise", okudagram)
This star system was only mentioned in writing.
It can't be deduced from the star chart in which quadrant Alpha Shiro was located as there were planets and star systems from both quadrants spread throughout the chart.
In the Bayer designation, which was a system of stellar classification, the Greek letter indicated the brightness of a star in a constellation. In this case, Beta Simmons would be the 2nd brightest star in its constellation.