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The Q-Star structures, also called as gray holes with a radius of two timesgreater than the corresponding Schwarzschild radius of same mass and from thecompact neutron star family with a very high density, have been obtained byusing a generalization of $q$-deformed fermions with two parameters $q$ and $p$as the constituents of the star. Because the interaction between particles arecontrolled by deformation parameters in $q,p$-fermions instead of a complicatedinteraction Lagrangian, we consider the deformation parameters giving themaximum Q-Star pressure between the interacting particles of stars. The coldand hot Q-Stars in temperatures of $T=0$, $T=40\ \mathrm{MeV}$ and $T=60\\mathrm{MeV}$ have been investigated from the numerical solutions of TOVequations and it is obtained that the Q-Stars can reach up to $13$ solar massand $75$ Km radius. Moreover, it is found that the total mass and radius of thestar increase when the star gets cool down, and a much denser state is reached.

Compact Q-Stars with q,p-Deformed Fermions