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The present work is devoted to the study of bosons evolving in the frozen magnetar’s crust endowed with an ultra-strong magnetic field orthogonal to an electric field,both described by periodic functions.We discuss the quantum tunneling process through the one-dimensional potential barrier along Oz.The solutions to the KleinGordon equation are expressed in terms of Mathieu’s functions which,for computable particle’s energy range,are ting from oscillatory to exponentially growing modes Mong Oz.Within the Jeffreys-Wentzel KramersBriIlouin framework,the transmission coefficient is computed for the particle momentum in the middle of the instability range.