Context. High-redshift blazars provide valuable input to studies of the evolution of active galactic nuclei (AGN) jets and provide constraints on cosmological models. Detections at high energies (0.1a< Ea< 100 GeV) of these distant sources are rare, but when they exhibit bright gamma-ray flares, we are able to study them. However, contemporaneous multi-wavelength observations of high-redshift objects (z">"4) during their different periods of activity have not been carried out so far. An excellent opportunity for such a study arose when the blazar TXS 1508+572 (z"="4.31) exhibited a γ-ray flare in 2022 February in the 0.1 300 GeV range with a flux 25 times brighter than the one reported in the in the fourth catalog of the Fermi Large Area Telescope. Aims. Our goal is to monitor the morphological changes, spectral index and opacity variations that could be associated with the preceding γ-ray flare in TXS 1508+572 to find the origin of the high-energy emission in this source. We also plan to compare the source characteristics in the radio band to the blazars in the local Universe (za< 0.1). In addition, we aim to collect quasi-simultaneous data to our multi-wavelength observations of the object, making TXS 1508+572 the first blazar in the early Universe (z">"4) with contemporaneous multi-frequency data available in its high state. Methods. In order to study the parsec-scale structure of the source, we performed three epochs of very-long-baseline interferometry (VLBI) follow-up observations with the Very Long Baseline Array (VLBA) supplemented with the Effelsberg 100-m Telescope at 15, 22, and 43 GHz, which corresponds to 80, 117, and 228 GHz in the rest frame of TXS 1508+572. In addition, one 86 GHz (456 GHz) measurement was performed by the VLBA and the Green Bank Telescope during the first epoch. Results. We present total intensity images from our multi-wavelength VLBI monitoring that reveal significant morphological changes in the parsec-scale structure of TXS 1508+572. The jet proper motion values range from 0.12 mas yr¹ to 0.27 mas yr¹, which corresponds to apparent superluminal motion β_app" 14.3 32.2.c. This is consistent with the high Lorentz factors inferred from the spectral energy distribution (SED) modeling for this source. The core shift measurement reveals no significant impact by the high-energy flare on the distance of the 43-GHz radio core with respect to the central engine, that means this region is probably not affected by e.g., injection of new plasma as seen in other well-studied sources like CTA 102. We determine the average distance from the 43-GHz radio core to the central supermassive black hole to be 46.1 ± 2.3.μas, that corresponds to a projected distance of 0.32 ± 0.02 pc. We estimate the equipartition magnetic field strength 1 pc from the central engine to be on the order of 1.8 G, and the non-equipartition magnetic field strength at the same distance to be about 257 G, the former of which values agrees well with the magnetic field strength measured in low to intermediate redshift AGN. Conclusions. Based on our VLBI analysis, we propose that the γ-ray activity observed in February 2022 is caused by a shock-shock interaction between the jet of TXS 1508+572 and new plasma flowing through this component. Similar phenomena have been observed, for example, in CTA 102 in a shock-shock interaction between a stationary and newly emerging component. In this case, however, the core region was also affected by the flare as the core shift stays consistent throughout the observations.

Context. PSO J334.2028+1.4075 (PSO J334) is a luminous quasar located at redshift z = 2.06. The source gained attention when periodic flux density variations were discovered in its optical light curve. These variations were initially interpreted as the variability due to the orbital motion of a supermassive black hole binary (SMBHB) residing in a single circumbinary accretion disk. The orbital separation was determined to be 0.006 pc with an in-spiral time of 7 yr in the rest frame of PSO J334. These findings suggested the quasar could be in the gravitational wave emitting phase of its merger and so extended multiwavelength observations were commenced. However, subsequent observations provided evidence against the binary hypothesis as no optical periodicity was found on extended time baselines. On the other hand, detailed radio analysis with the Karl G. Jansky Very Large Array (VLA) and the Very Long Baseline Array (VLBA) revealed a lobe-dominated quasar at kiloparsec scales, and possibly a precessing jet, which could retain PSO J334 as a binary SMBH candidate. Aims. We aim to study both the large- and small-scale radio structures in PSO J334 to provide additional evidence for or against the binary scenario. Methods. We observed the source at 1.7 GHz with the European Very Long Baseline Interferometry Network (EVN), and at 1.5 and 6.2 GHz with the VLA, at frequencies that complement the previous radio interferometric study. Results. Our images reveal a single component at parsec scales slightly resolved in the southeast-northwest direction and a lobe-dominated quasar at kiloparsec scales with a complex structure. The source morphology and polarization in our VLA maps suggest that the jet is interacting with dense clumps of the ambient medium. While we also observe a misalignment between the inner jet and the outer lobes, we suggest that this is due to the restarted nature of the radio jet activity and the possible presence of a warped accretion disk rather than due to the perturbing effects of a companion SMBH. Conclusions. Our analysis suggests that PSO J334 is most likely a jetted active galactic nucleus with a single SMBH, and there is no clear evidence of a binary SMBH system in its central engine.