We present the results of optical spectroscopy for 19 quasar candidates at photometric redshifts $zphot gtrsim 3$, Nobs of which enter into the Khorunzhev et al.~(2016) catalog (K16). This is a catalog of quasar candidates and known type 1 quasars selected among the X-ray sources of the textit{3XMM-DR4}catalog of the XMM-Newton serendipitous survey. We have performed spectroscopy for a quasi-random sample of new candidates at the 1.6-m Azt telescope of the Sayan Solar Observatory and the 6-m BTA telescope of the Special Astrophysical Observatory. The spectra at Azt were taken with the new low- and medium-resolution ADAM spectrograph that was produced and installed on the telescope in 2015. Fourteen of the Nobs candidates actually have turned out to be quasars; 10 of them are at spectroscopic redshifts z > 3. The high purity of the sample of new candidates suggests that the purity of the entire K16 catalog of quasars is probably 70--80%. One of the most distant ($zspec=5.08$) optically bright ($i^primelesssim 21$) quasars ever detected in X-ray surveys has been discovered.