  This work is motivated by the sign problem in a logarithmic parameter of
black hole entropy and the existing more massive white dwarfs than the
Chandrasekhar mass limit. We examine the quadratic, linear, and
linear-quadratic generalized uncertainty principle (GUP) models within the
virtue of recent masses and radii of white dwarfs. We consider the modification
generated by introducing the minimal length proposal on the degenerate Fermi
gas equation of state (EOS) and on the hydrostatic equation. For the latter, we
applied Verlinde's proposal regarding entropic gravity to derived the quantum
corrected Newtonian gravity which in turn responsible for modifying the
hydrostatic equation. Through the chi-square analysis of the models, we have
found that the observation data favor the quadratic dan linear GUP models
without mass limit. However, for the quadratic-linear GUP model, we can obtain
the positive value of the free parameter $\gamma_0$ as well as we can get mass
limit more massive than the Chandrasekhar mass limit. In the linear-quadratic
GUP model, the formation of stable massive white dwarfs than the Chandrasekhar
limit is possible only if both parameters are not equal.
