GHz-peaked spectrum (GPS) objects are compact and powerful radio sources (galaxies and quasars) that have a maximum in the radio spectrum in the range from hundreds of MHz to several GHz. These sources are interesting as precursors of radio galaxies and, at high redshifts, also as active galactic nuclei of the early Universe. A monitoring of a sample of 101 bright (with a flux density of more than 100 mJy at a frequency of 1.4 GHz) quasars at high redshifts ($z >$ 3) with the RATAN-600 radio telescope in 2017-2020 at six frequencies (1.2-22.3 GHz) has revealed that almost half of the objects (47%) have a radio spectrum with the maximum at GHz frequencies. We studied their radio properties and determined 10 new candidates for GPS sources based on their estimated peak frequencies, low variability, and radio morphology from the literature.