  We searched for high-z quasars within the X-ray source population detected in
the contiguous $\sim 140^2$ eFEDS field observed by eROSITA during the
performance verification phase. We collected the available spectroscopic
information in the field, including the sample of all currently known optically
selected z>5.5 quasars and cross-matched secure Legacy DR8 counterparts of
eROSITA-detected X-ray point-like sources with this spectroscopic sample. We
report the X-ray detection of an eROSITA source securely matched to the
well-known quasar SDSS J083643.85+005453.3 (z=5.81). The soft X-ray flux of the
source derived from eROSITA is consistent with previous Chandra observations.
In addition, we report the detection of the quasar with LOFAR at 145 MHz and
ASKAP at 888 MHz. The reported flux densities confirm a spectral flattening at
lower frequencies in the emission of the radio core, indicating that the quasar
could be a (sub-) gigahertz peaked spectrum source. The inferred spectral shape
and the parsec-scale radio morphology of SDSS J083643.85+005453.3 suggest that
it is in an early stage of its evolution into a large-scale radio source or
confined in a dense environment. We find no indications for a strong jet
contribution to the X-ray emission of the quasar, which is therefore likely to
be linked to accretion processes. The detection of this source allows us to
place the first constraints on the XLF at z>5.5 based on a secure spectroscopic
redshift. Compared to extrapolations from lower-redshift observations, this
favours a relatively flat slope for the XLF at $z\sim 6$ beyond $L_*$. The
population of X-ray luminous AGNs at high redshift may be larger than
previously thought. From our XLF constraints, we make the conservative
prediction that eROSITA will detect $\sim 90$ X-ray luminous AGNs at redshifts
5.7<z<6.4 in the full-sky survey (De+RU).
