  We construct the eROSITA X-ray catalog of radio galaxies discovered by the
WERGS survey that is made by the cross-matching of the wide-area Subaru/HSC
optical survey and VLA/FIRST 1.4 GHz radio survey. We find 393 eROSITA detected
radio galaxies in the 0.5--2 keV band in the eFEDS field covering 140~deg$^2$.
Thanks to the wide and medium depth eFEDS X-ray survey, the sample contains the
rare and most X-ray luminous radio galaxies above the knee of the X-ray
luminosity function, spanning 44<log L(0.5-2keV,abs)<46.5 at $1<z<4$. Based on
the X-ray properties obtained by the spectral fitting, 37 sources show obscured
AGN signature with $\log (N_\mathrm{H}/\mathrm{cm}^{-2})>22$. Those obscured
and radio AGN reside in $0.4<z<3.2$, indicating that they are obscured
counterparts of the radio-loud quasar, which are missed in the previous optical
quasar surveys. By combining radio and X-ray luminosities, the jet production
efficiency $\eta_\mathrm{jet}$ is investigated, and we find 14 sources with
extremely high jet production efficiency at $\eta_\mathrm{jet}\approx1$. This
high $\eta_\mathrm{jet}$ value might be a result of 1) the decreased radiation
efficiency of $\eta_\mathrm{rad}<0.1$ due to the low accretion rate for those
sources and/or 2) the boosting due to the decline of $L_\mathrm{bol}$ by a
factor of 10--100 by keeping $P_\mathrm{jet}$ constant in the previous Myr,
indicating the experience of the AGN feedback. Finally, inferring the BH masses
from the stellar-mass, we find that X-ray luminous sources show the excess of
the radio emission with respect to the value estimated from the fundamental
plane. Such radio emission excess cannot be explained by the Doppler booming
alone, and therefore disk-jet connection of X-ray luminous eFEDS-WERGS is
fundamentally different from the conventional fundamental plane which mainly
covers low accretion regime.
