The tunability aspect of the electronic properties induced by the magnetic field and optical phonon in Beta-borophene on the polar substrate (ZrO2) is reported in the paper. To calculate the ground state of the electron-phonon system, we present the analytical method within the frame of the Lee-Low-Pines theory. In the theoretical investigation of the polaron formation in -borophene, we describe its renormalized effective masses and fermi velocities which have different in each coordinate due to out-of-plane buckling structure. We have used average renormalized effective mass and fermi velocities, the charge carriers in buckling structure are affected by the external magnetic field. It is analytically shown that polaronic energy has the momentum dependent nature as a function of energy.