  Radio-loud quasars at high redshift (z > 4) are rare objects in the Universe
and rarely observed with Very Long Baseline Interferometry (VLBI). But some of
them have flux density sufficiently high for monitoring of their apparent
position. The instability of the astrometric positions could be linked to the
astrophysical process in the jetted active galactic nuclei in the early
Universe. Regular observations of the high-redshift quasars are used for
estimating their apparent proper motion over several years. We have undertaken
regular VLBI observations of several high-redshift quasars at 2.3 GHz (S band)
and 8.4 GHz (X band) with a network of five radio telescopes: 40-m Yebes
(Spain), 25-m Sheshan (China), and three 32-m telescopes of the Quasar VLBI
Network (Russia) -- Svetloe, Zelenchukskaya, and Badary. Additional facilities
joined this network occasionally. The sources have also been observed in three
sessions with the European VLBI Network (EVN) in 2018--2019 and one Long
Baseline Array (LBA) experiment in 2018. In addition, several experiments
conducted with the Very Long Baseline Array (VLBA) in 2017--2018were used to
improve the time sampling and the statistics. Based on these 37 astrometric
VLBI experiments between 2017 and 2021, we estimated the apparent proper
motions of four quasars: 0901+697, 1428+422, 1508+572, and 2101+600.
