  Black holes with dyonic charges in Einstein-Maxwell-dilaton-axion
supergravity theory are revisited in the context of black hole shadows. We
consider static as well as rotating (namely the dyonic Kerr-Sen) black holes.
The matter stress-energy tensor components, sourced by the Maxwell, axion and
dilaton fields satisfy the standard energy conditions. The analytical
expressions for the horizon and the shadow radius of the static spacetimes
demonstrate their dependence on $P^2+Q^2$ ($P$, $Q$ the magnetic and electric
charges, respectively) and the mass parameter $M$. The shadow radius lies in
the range $2M <R_{shadow}<3\sqrt{3} M$ and there is no stable photon orbit
outside the horizon. Further, shadows cast by the rotating dyonic Kerr-Sen
black holes are also studied and compared graphically with their Kerr-Newman
and Kerr-Sen counterparts. Deviation of the shadow boundary is prominent with
the variation of the magnetic charge, for the relatively slowly rotating dyonic
Kerr-Sen spacetimes. We test any possible presence of a magnetic monopole
charge in the backdrop of recent EHT observations for the supermassive black
holes M87$^*$ and Sgr A$^*$. Deviation from circularity of the shadow boundary
($\Delta C$) and deviation of the average shadow radius from the Schwarzschild
shadow radius (quantified as the fractional deviation parameter $\delta$) are
the two observables used here. Observational bound on $\Delta C$ (available
only for M87$^*$) is satisfied for all theoretically allowed regions of
parameter space and thus cannot constrain the parameters. The observational
bound on $\delta$ available for Sgr A$^*$ translates into an upper limit on any
possible magnetic monopole charge linked to Sgr A$^*$ and is given as
$P\lesssim 0.873\, M$. Such a constraint on $P$ is however expected to be far
more stringent for other astrophysical tests.
