  In this paper we consider 6-superlinear Chern-Simons-Schr\"{o}dinger systems.
In contrast to most studies, we consider the case where the potential $V$ is
indefinite so that the Schr\"{o}dinger operator $-\Delta +V$ possesses a
finite-dimensional negative space. We obtain nontrivial solutions for the
problem via Morse theory.
