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The object of this paper is study $(\epsilon)$-para-Sasakian 3-manifolds satisfying certain conditions on the $\mathcal{Z}$ tensor. We characterize, $\mathcal{Z}$-symmetric; $\mathcal{Z}$-semisymmetric; $\mathcal{Z}$-pseudosymmetric; and projectively $\mathcal{Z}$-semisymmetric conditions on an $(\epsilon)$-para-Sasakian 3-manifold.

$\mathcal{Z}$-symmetries of $(\epsilon)$-para-Sasakian 3-manifolds