  During its calibration and performance verification phase, the eROSITA
instrument aboard the SRG satellite performed a uniform wide--area X-ray survey
of approximately 140 deg$^{2}$ in a region of the sky known as the eROSITA
Final Equatorial Depth Survey (eFEDS). The primary aim of eFEDS is to
demonstrate the scientific performance to be expected at the end of the 8-pass
eROSITA all sky survey. This will provide the first focussed image of the whole
sky in the hard X-ray ($>2$~keV) bandpass. The expected source population in
this energy range is thus of great interest, particularly for AGN studies. We
use the 2.3--5 keV selection presented by Brunner et al. (2022) to construct a
sample of 246 point-like hard X-ray sources for further study and
characterization. These are classified as either extragalactic ($\sim 90$~\%)
or Galactic ($\sim 10$~\%), with the former consisting overwhelmingly of AGN
and the latter active stars. We concentrate our further analysis on the
extragalactic/AGN sample, describing their X-ray and multiwavelength properties
and comparing them to the eFEDS main AGN sample selected in the softer 0.2-2.3
keV band. The eROSITA hard band selects a subsample of sources that is a factor
$>10$ brighter than the eFEDS main sample. The AGN within the hard population
reach up to $z=3.2$ but on the whole are relatively nearby, with median
$z$=0.34 compared to $z$=0.94 for the main sample. The hard survey probes
typical luminosities in the range $\log L_{\rm X} = 43-46$. X-ray spectral
analysis shows significant intrinsic absorption (with $\log N_{\rm H}>21$) in
$\sim 20$~\% of the sources, with a hard X-ray power law continuum with mean
$<\Gamma>=1.83\pm0.04$, typical of AGN, but slightly harder than the
soft-selected eROSITA sample. (abridged)
