History and specifics
The Terminimurus vicinity was in in area claimed by the Romulan Star Empire in the 23rd century of the Kelvin timeline, in the vicinity of D'Deridex and, outside of Romulan space, Earokij, Tiwoqua and Piuioab. (ST video game: Fleet Command)
While Fleet Command does not establish quadrant locations for game settings, the placement within the Romulan Star Empire strongly indicates that this system is in the galaxy's Beta Quadrant. However, the fact that some parts of Romulan space cross into the Alpha Quadrant in other sources casts doubt on that being sufficient evidence to definitively state a quadrant location for the purposes of this wiki.