The Polyakov-Nambu-Jona-Lasinio~(PNJL) effective quark model incorporates the confinement/deconfinement phase-transition in the original Nambu-Jona-Lasinio model~(NJL) by inserting the Polyakov Loop~($\Phi$) in the equations of state~(EOS) at finite temperature. However, at zero temperature regime, the PNJL model loses all contributions from $\Phi$ and the EOS return to the original NJL ones at $T=0$. In this work, we present the SU(3) PNJL model at zero temperature, called SU(3) PNJL0. The model is based on the modification of coupling constants, by making them dependent on $\Phi$ and adding one term function of $\Phi$ in the grand canonical potential density, which limits the loop within $0 \le \Phi \le 1$ and favors a nonvanishing $\Phi$ solution. We impose that in the free quark regime~(deconfinement region) all interactions vanish. We investigate the first order phase transition and how the strange quark favors the restoration of chiral symmetry. Another point discussed is how the constants $G_V$ and $a_3$~(a parameter in the Polyakov potential) affect the quarkyonic phase of this model.