  In the present work, we apply Tsallis non-extensive statistics to study the
thermodynamic properties and phase diagram of quark matter in the Polyakov
chiral SU(3) quark mean field model. Within this model, the properties of the
quark matter are modified through the scalar fields $\sigma, \zeta, \delta,
\chi$, the vector fields $\omega, \rho$, $\phi$, and the Polyakov fields $\Phi$
and $\bar{\Phi}$ at finite temperature and chemical potential. Non-extensive
effects have been introduced through a dimensionless parameter $q$ and the
results are compared to the extensive case ($q\rightarrow1$). In the
non-extensive case, the exponential in the Fermi-Dirac (FD) function is
modified to a $q$-exponential form. The influence of $q$ parameter on the
thermodynamic properties: pressure, energy, and entropy density as well as
trace anomaly is investigated. The speed of sound and specific heat with
non-extensive effects is also studied. Furthermore, the effect of
non-extensivity on the deconfinement phase transition as well as the chiral
phase transition of $u, d,$ and $s$ quarks is explored. We found that the
critical end point (CEP), which defines the point in the $(T - \mu)$ phase
diagram where the order of the phase transition changes, shifts to a lower
value of temperature, $T_{CEP}$, and a higher value of chemical potential,
$\mu_{CEP}$, as the non-extensivity is increased, i.e., $q>$1.
