  We study N=2 supersymmetric Chern-Simons Higgs models in $(2+1)$-dimensions
and the existence of extended underlying supersymmetric quantum mechanics
algebras. Our findings indicate that the fermionic zero modes quantum system in
conjunction with the system of zero modes corresponding to bosonic
fluctuations, are related to an N=4 extended 1-dimensional supersymmetric
algebra with central charge, a result closely connected to the N=2 spacetime
supersymmetry of the total system. We also add soft supersymmetric terms to the
fermionic sector in order to examine how this affects the index of the
corresponding Dirac operator, with the latter characterizing the degeneracy of
the solitonic solutions. In addition, we analyze the impact of the underlying
supersymmetric quantum algebras to the zero mode bosonic fluctuations. This is
relevant to the quantum theory of self-dual vortices and particularly for the
symmetries of the metric of the space of vortices solutions and also for the
non-zero mode states of bosonic fluctuations.
