This paper addresses the effect of a generalized uncertainty principle produced by different approaches of quantum gravity within the Planck scale on statistical and thermodynamical properties of ideal fermion and boson gases. The partition function and some thermodynamical properties are investigated. The Bose–Einstein condensation and the ground state properties of fermion gases are also considered. The target approach is extended to a white dwarf as an application. The modified mass-radius relation is calculated. A decrease in the pressure of degenerate fermions due to the presence of quantum gravity leads to a contraction in the star radius. It is also found that the gravity background does not result in any change in white dwarf stability.