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Nonlinear electrodynamics is known as the generalizations of Maxwellelectrodynamics at strong fields and presents interesting features such ascuring the classical divergences present in the linear theory when coupled togeneral relativity. In this paper, we consider the asymptotically flatReissner-Nordstr\"om black hole solution with higher-order magnetic correctionin Einstein-nonlinear-Maxwell fields. We study the effect of the magneticcharge parameters on the black hole, viz. weak deflection angle of photons andmassive particles using Gauss-bonnet theorem. Moreover, we apply theKeeton-Petters formalism to confirm our results of the weak deflection angle.Apart from vacuum, their influence in the presence of different media such asplasma and dark matter are probed as well. Finally, we examine the black holeshadow cast using the null-geodesics method and investigate its sphericallyin-falling thin accretion disk. Our inferences show how the magnetic chargeparameter $p$ affects the other physical quantities; so, we impose someconstraints on this parameter using the observations from the Event HorizonTelescope.

Deflection angle and shadow of the Reissner-Nordstr\"om black hole with higher-order magnetic correction in Einstein-nonlinear-Maxwell fields