There is still a limited number of high-redshift (z > 3) active galactic nuclei (AGNs) whose jet kinematics have been studied with very long baseline interferometry (VLBI). Without a dedicated proper motion survey, regularly conducted astrometric VLBI observations of bright radio-emitting AGN with sensitive arrays can be utilized to follow changes in the jets, by means of high-resolution imaging and brightness distribution modelling. Here, we present a first-time VLBI jet kinematic study of NVSS J080518 + 614423 (z = 3.033) and NVSS J165844-073918 (z = 3.742), two flat-spectrum radio quasars that display milliarcsecond-scale jet morphology. Archi v al astrometric observ ations carried out mainly with the Very Long Baseline Array, supplemented by recent data taken with the European VLBI Network, allowed us to monitor changes in their radio structure in the 7.6-8.6 GHz frequency band, covering almost two decades. By identifying individual jet components at each epoch, we were able to determine the apparent proper motion for multiple features in both sources. Apparent superluminal motions range (1-14) c, and are found to be consistent with studies of other high-redshift AGN targets. Using the physical parameters derived from the brightness distribution modelling, we estimate the Doppler-boosting factors (δ≈11.2 and δ≈2.7), the Lorentz factors (Γ ≈7.4 and Γ ≈36.6), and the jet viewing angles (θ≈4.4°and θ≈8.0°), for NVSS J080518 + 614423 and NVSS J165844-073918, respectively. The data revealed a stationary jet component with negligible apparent proper motion in NVSS J165844-073918.

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 in 2018-2019 and one Long Baseline Array experiment in 2018. In addition, several experiments conducted with the Very Long Baseline Array in 2017-2018 were 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.

We present and briefly discuss results of several studies of the source J2102+6015 with tentatively defined redshift z = 4.575 which demonstrates unusual properties in imaging and astrometric VLBI observations. Its properties might be considered as indications on the supermassive black hole binary which can be considered as a so far rare example of a high-redshift source of known electromagnetic and, possibly, predictable gravitational wave emissions.