Our aim is to increase the limited number of quasars behind M 31, necessary for probing the chemical content of the gas and for proper motion reference, with reliable and homogeneous redshift measurements from emission lines. We carried out spectroscopic follow-up of 32 quasar candidates. We confirm 23 quasars. Two are new discoveries (J004029.727+403705.68 and J004215.489+412031.52) and the rest have been reported elsewhere, but with somewhat deficient analysis; 16 spectra are published for the first time. We report new homogeneous redshifts for 34 quasars (from 40 spectra, adding 17 from the archives) and summarize all available information about bona fide quasars with reliable redshift, bringing their number to 124 within the {mu}B=26m/arcsec^2^ isophote. We carried out a comparison of redshifts from different sources and excluded some objects with redshifts derived from low-resolution spectra. We derived the reddening for them from the color excess with respect to dereddened counterparts with similar redshifts in the field. Comparisons of our reddenings with M 31 reddening maps found no significant correlations. Most QSOs behind M 31 show low reddening and do not probe high extinctions, probably due to a bias toward following up brighter and less extinct candidates, which underlines the need to identify fainter quasars behind nearby galaxies, especially behind higher extinction regions. Finally, the redshifts derived from low-resolution spectra must be treated with caution because they can contain significant errors.