  Nonlinear electrodynamics is known as the generalizations of Maxwell
electrodynamics at strong fields and presents interesting features such as
curing the classical divergences present in the linear theory when coupled to
general relativity. In this paper, we consider the asymptotically flat
Reissner-Nordstr\"om black hole solution with higher-order magnetic correction
in Einstein-nonlinear-Maxwell fields. We study the effect of the magnetic
charge parameters on the black hole, viz. weak deflection angle of photons and
massive particles using Gauss-bonnet theorem. Moreover, we apply the
Keeton-Petters formalism to confirm our results of the weak deflection angle.
Apart from vacuum, their influence in the presence of different media such as
plasma and dark matter are probed as well. Finally, we examine the black hole
shadow cast using the null-geodesics method and investigate its spherically
in-falling thin accretion disk. Our inferences show how the magnetic charge
parameter $p$ affects the other physical quantities; so, we impose some
constraints on this parameter using the observations from the Event Horizon
Telescope.
