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We study the infrared phases of $\mathcal{N}\,=\,1$ QCD$_3$ with gauge group$SU(N_c)$ and with the superpotential containing the mass term and the baryonoperator. We restrict ourselves to the cases, when the number of flavors isequal to the number of colours, such that baryon operator is neutral under theglobal $SU(N_F)$. We also focus on the cases with two, three and four colours,such that the theory is perturbatively renormalizable. On the $SU(2)$ phasediagram we find two distinct CFTs with $\mathcal{N}\,=\,2$ supersymmetry,already known from the phase diagram of $SU(2)$ theory with one flavor. As forthe $SU(3)$ phase diagram, consistency arguments lead us to conjecture thatalso there supersymmetry enhancement to $\mathcal{N}\,=\,2$ must occur.Finally, similar arguments lead us to conclude that also for the $SU(4)$ casewe should observe supersymmetry enhancement at the fixed point. Yet, we findthat this conclusion would be in contradiction with the renormalization groupflow analysis. We relate this inconsistency between the two kinds of argumentsto the fact that the theory is not UV complete.

Notes on $\mathcal{N}=1$ QCD$_3$ with baryon superpotential