  In a $(2+1)$-dimensional Maxwell-Chern-Simons theory coupled with a fermion
and a scalar, which has $\mathcal{N}=2$ SUSY in absence of the boundary, the
insertion of a spatial boundary breaks the supersymmetry. We show that only a
subset of the boundary conditions allowed by the self-adjointness of the
Hamiltonian can preserve partial $\mathcal{N}=1$ supersymmetry, while for the
remaining boundary conditions SUSY is completely broken. In the latter case, we
demonstrate two distinct SUSY-breaking mechanisms. For some of the
SUSY-breaking boundary conditions, the SUSY variation of the action does not
vanish which explicitly breaks SUSY. While for certain other boundary
conditions, despite the invariance of action under SUSY transformations,
unpaired fermionic edge states in the domain of the Hamiltonian leads to an
anomalous breaking of the supersymmetry.
