  In this paper, we study thermodynamical contributions to the theory of
gravity under the $q$-deformed boson and fermion gas models. According to the
Verlinde's proposal, the law of gravity is not based on a fundamental
interaction but it emerges as an entropic force from the changes of entropy
associated with the information on the holographic screen. In addition,
Strominger shows that the extremal quantum black holes obey neither boson nor
fermion statistics, but they obey deformed statistic. Using these notions, we
find $q$-deformed entropy and temperature functions. We also present the
contributions that come from the $q$-deformed model to the Poisson equation,
Newton's law of gravity and Einstein's field equations.
