  Based on a comparison of the SRG/eROSITA catalog of X-ray active stars and
the Gaia catalog, a sample of 502 peculiar objects was obtained for which Gaia,
on one hand, detects statistically significant values of parallax or proper
motion and, on the other hand, registers signs of the non zero source extent in
the optical band. In the log ($F_X/F_{\rm opt}$) - (G-RP) color diagram these
objects are separated from the balk of X-ray active stars and are located in
the region typical for the galaxies with active nuclei. According to the SIMBAD
database, about $\sim 50$% of them are confirmed AGNs and galaxies with
spectroscopically measured redshifts, and only $\sim$1.4% are confirmed
Galactic objects. Spectroscopic observations of 19 unidentified objects on the
RTT-150 telescope demonstrated, that 18 of them are AGNs at redshifts
$\sim$0.01-0.3, and one object is a M star in our Galaxy. We discuss various
scenarios explaining the nature of such peculiar objects.
