  The effect of statistics of the quasiparticles in the nuclear matter at
extreme conditions of density and temperature is evaluated in the relativistic
mean-field model generalized to the framework of the fractional exclusion
statistics (FES). In the model, the nucleons are described as quasiparticles
obeying FES and the model parameters were chosen to reproduce the ground state
properties of the isospin-symmetric nuclear matter. In this case, the
statistics of the quasiparticles is related to the strengths of the
nucleon-nucleon interaction mediated by the neutral scalar and vector meson
fields. The relevant thermodynamic quantities were calculated as functions of
the nucleons density, temperature and fractional exclusion statistics parameter
$\alpha$. It has been shown that at high temperatures and densities the
thermodynamics of the system has a strong dependence on the statistics of the
particles. The scenario in which the nucleon-nucleon interaction strength is
independent of the statistics of particles was also calculated, but it leads in
general to unstable thermodynamics.
