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–Nordström 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 the Gauss–Bonnet theorem. Moreover, we apply Keeton–Petters formalism to confirm our results concerning the weak deflection angle. Apart from a 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 observations from the Event Horizon Telescope.