We present a spectroscopic study of eight extremely low-metallicity candidate emission-line galaxies with oxygen abundances possibly below 12 + log O/H = 7.35. These galaxies were selected from data release 10 of the Sloan Digital Sky Survey/Baryon Oscillation Spectroscopic Survey (SDSS/BOSS DR10). We will call these extremely metal-deficient (XMD) galaxies. The electron temperaturesensitive emission line [O iii] λ4363 is detected in three galaxies and marginally detected in two galaxies, allowing for abundance determination by a "direct" method. Because of large uncertainties in the [O iii]λ4363 Å line fluxes, we also calculated oxygen abundance in these galaxies together with the remaining three galaxies using a strong-line semi-empirical method. This method gives oxygen abundances higher than 7.35 for three galaxies with detected [O iii]λ4363 Å line and lower than 7.35 for the remaining five objects of the sample. The newly-discovered galaxies represent excellent targets for follow-up spectroscopic observations with the largest telescopes to improve the oxygen abundance determination and to increase the number of these very rare low-metallicity objects. The extreme location of the most massive and luminous XMD galaxies and XMD candidates in the stellar mass-metallicity diagram implies that these galaxies may be genuine young objects. With stellar masses of up to ∼10 7 -10 8 M , the galaxies are not chemically enriched and strongly deviate to lower metallicity as compared to the relation obtained for a large sample of low-redshift, star-forming galaxies.