In the last paper, we introduced a new curvaturlike tensor field in an almost contact Riemannian manifold and we showed some geometrical properties of this tensor field in a Kenmotsu and a Sasakian manifold. In this paper, we define another new curvaturelike tensor field, named $(\CHR)_3$-curvature tensor in an almost contact Riemannian manifold which is called a contact holomorphic Riemannian curvature tensor of the second type. Then, using this tensor, we mainly research $(\CHR)_3$-curvature tensor in a Sasakian manifold. Then we define the notion of the flatness of a $(\CHR)_3$-curvature tensor and we show that a Sasakian manifold with a flat $(\CHR)_3$-curvature tensor is flat. Next, we introduce the notion of $(\CHR)_3$-$\eta $-Einstein in an almost contact Riemannian manifold. In particular, we show that Sasakian $(\CHR)_3$-$\eta $-Einstein manifold is $\eta$-Einstain. Moreover, we define the notion of $(\CHR)_3$-space form and consider this in a Sasakian manifold. Finally, we consider a conformal transformation of an almost contact Riemannian manifold and we get new invariant tensor fields (not the conformal curvature tensor) under this transformation. Finally, we prove that a conformally $(\CHR)_3$-flat Sasakian manifold does not exist.