The object of the present paper is to study φ−Ricci symmetric and locally φ−Ricci symmetric 3-dimensional quasi-Sasakian manifolds with structure function β =constant. Also we study η−parallel Ricci tensor and cyclic parallel Ricci tensor with β =constant. Applications of such manifold have been considered. The existence of 3-dimensional φ−Ricci symmetric and locally φ−Ricci symmetric quasi-Sasakian manifolds are also given by concrete examples.