Beta Rigel was a location in the Alpha Quadrant.
This location was only mentioned in writing.
The map on which this location appeared was inspired by Star Trek: Star Charts (p. 62) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"). Star Trek: Star Charts was the first to identify this location as a star, explaining on p. 59 that it is distinct from the "true" Rigel, by which it means the real star of that name. According to p. 52, this Rigel is host to Rigel IV as well as Rigel X, the Rigel Colony visited by Enterprise on its maiden voyage. As such, the existence of Beta Rigel fixes an issue, as the real Rigel is very remote, given as 773 ly away in the book but more recently estimated at around 863 ly, whereas "Broken Bow" is set before "Two Days and Two Nights", which establishes that Enterprise is about 90 ly from home and as such has traveled as far as any Human has ever traveled from Earth. Furthermore, a situation where there are two Rigels explains how there could be both many populated and popular planets with the name Rigel, some apparently even containing Human populations, and yet also seemingly remote and far from civilization planets such as Rigel VII and Rigel XII.
According to Star Trek: Star Charts (p. 62) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), Beta Rigel was an A-class star.