  We consider a static black hole immersed in the Power-Yang-Mills field in
four dimensional Einstein-Gauss-Bonnet gravity and investigate the effect of
various parameters on the radius of the photon sphere. The modified form of the
Newman-Janis algorithm is used for obtaining a rotating black hole solution in
this gravity. Further, we try to explore the influence of the Yang-Mills
magnetic charge $Q$ with power $q$, Gauss-Bonnet parameter $\alpha$ and spin
$a$ on the horizon radius. The geodesic equations are constructed by
incorporating the Hamilton-Jacobi formalism. The radial component of the
geodesic equations gives the effective potential which is further used in
deriving the mathematical structure for the shadows by using Bardeen's
procedure for a fixed observer at infinity. The shadows are calculated and
plotted in terms of two celestial coordinates for an equatorial observer. It is
observed that all the parameters have a very significant effect on the shadow
and related physical observables. {We also obtain the constraint values for the
spin, magnetic charge and Gauss-Bonnet parameters, using the shadow size of
supermassive black holes Sagittarius A$^*$ and M$87$* from the EHT observations
for the cases of $q=0.6$ and $0.9$. It is shown that there are upper and lower
bounds for the charge and spin of M$87$* at $q=0.6$, while only the upper
bounds for charge and spin of Sagittarius A$^*$. Finally, we investigate the
energy emission rate in the Hawking radiation around the $4D$
Einstein-Gauss-Bonnet black hole in the Power-Yang-Mills field.}
