The Orion OB1a sub-association is a rich low-mass star (LMS) region. Previous spectroscopic studies have confirmed 160 LMSs in the 25 Orionis stellar group (25 Ori), which is the most prominent overdensity of Orion OB1a. Nonetheless, the current census of the 25 Ori members is estimated to be lower. than 50% complete, leaving a large number of members to be still confirmed. We retrieved 172 low-resolution stellar spectra in Orion OB1a observed as ancillary science in the SDSS-III/BOSS survey, for which we classified their spectral types and determined physical parameters. To determine memberships, we analyzed the H-alpha emission, Li I lambda 6708 absorption, and Na I lambda lambda 8183, 8195 absorption as youth indicators in stars classified as M type. We report 50 new LMSs spread across the 25 Orionis, ASCC 18, and ASCC 20 stellar groups with spectral types from M0 to M6, corresponding to a mass range of 0.10 <= m/M-circle dot <= 0.58. This represents an increase of 50% in the number of known LMSs in the area and a net increase of 20% in the number of 25 Ori members in this mass range. Using parallax values from the Gaia DR1 catalog, we estimated the distances to these three stellar groups and found that they are all co-distant, at 338 +/- 66 pc. We analyzed the spectral energy distributions of these LMSs and classified their disks into. evolutionary classes. Using H-R diagrams, we found a suggestion that 25 Ori could be slightly older than. the other two observed groups in Orion OB1a.