A catalog of quasar candidates at redshifts 3<z<5.5 is presented. These candidates have been selected among X-ray sources in the XMM-Newton Serendipitous Source Catalog (3XMM-DR4) in the 0.5-2keV band, located at high galactic latitudes |b|>20deg in the Sloan Digital Sky Survey (SDSS) area. The total overlapping area is about 300 sq. deg. The SDSS, 2MASS and WISE photometric catalogs were used. Only SDSS point sources were considered. X-ray sources having an optical counterpart with magnitude error in SDSS z band of less than 0.2 and color i-z<0.6 were chosen. Their photometric redshifts were determined with the EAZY code using a library of spectral templates. A sample of quasar candidates with photometric redshifts in the range 2.75<z<5.5 has been composed. Objects whose spectral energy distributions are better described by stellar templates have been excluded. The selection completeness of known quasars is about 80%. The normalized median absolute deviation of the differences between the photometric and spectroscopic redshifts of known quasars is 0.07 (with 9% outliers). The sky density of quasar candidates in our sample is 1.5 times that of the spectroscopic SDSS sample in the same fields. Follow-up spectroscopy should clarify the purity of the sample.