  We selected sources with a steep soft-X-ray-band spectrum with a photon index
larger than 2.5 -- measured by eROSITA on board the Spectrum-Roentgen-Gamma
(SRG) -- from the eFEDS AGN catalogue as candidates of highly accreting
supermassive black holes, and investigated their multi-wavelength properties.
Among 601 bright AGN with 0.2-5 keV counts of greater than 100, 83 sources
(~14%) are classified as steep-spectrum sources. These sources have typical
0.5-2 keV luminosities of L(SX) ~ 1e44 erg/s and the majority of them are found
at redshifts below z=1. In comparison with sources with flatter spectra, these
sources have, on average, a UV (or optical) to 2 keV luminosity ratio that is
larger by ~0.3 dex and bluer optical-to-UV continuum emission. They also appear
to be radio quiet based on the detection rate in the FIRST and VLASS surveys.
Their host galaxies -- at least in the redshift range of z=0.2-0.8, where the
AGN-galaxy decomposition results from the Subaru Hyper Suprime-Cam imaging are
available -- tend to be late-type and have smaller stellar masses than those of
sources with flatter spectra. These properties are similar to those found in
nearby narrow-line Seyfert 1 galaxies, in agreement with the picture that they
are AGN with elevated accretion rates and are in the early growth phase of
black hole and galaxy co-evolution. However, the steep-spectrum sources are not
exclusively narrow-line Seyfert 1 galaxies; indeed many are broad-line Seyfert
1 galaxies, as found by a catalogue search. This suggests that these
steep-spectrum sources may be black holes generally with high accretion rates
but of a wide mass range, including a few objects emitting at L(SX)>1e45 erg/s,
of which black hole masses can be close to 10^9 M_sun.
