We study the geometry of half lightlike submanifolds $(M,g,S(TM),S(TM^\perp))$ of a semi-Riemannian manifold $(\widetilde{M},\tilde{g})$ of quasi-constant curvature subject to the following conditions; (1) the curvature vector field $\zeta$ of $\widetilde M$ is tangent to $M$, (2) the screen distribution $S(TM)$ of $M$ is either totally geodesic or totally umbilical in $M$, and (3) the co-screen distribution $S(TM^\perp)$ of $M$ is a conformal Killing distribution.