  We discuss a supersymmetric extension of a non-relativistic Chern-Simons
matter theory, known as the SUSY Jackiw-Pi model, in a harmonic trap. We show
that the non-relativistic version of the superconformal symmetry, called the
super-Schr\"odinger symmetry, is not spoiled by an external field including the
harmonic potential. It survives as a modified symmetry whose generators have
explicit time dependences determined by the strength of the trap, the rotation
velocity of the system and the fermion number chemical potential. We construct
1/3 BPS states of trapped Jackiw-Pi vortices preserving a part of the modified
superconformal symmetry and discuss fluctuations around static BPS
configurations. In addition to the bosonic massive Nambu-Goldstone modes, we
find that there exist massive Nambu-Goldstone fermions associated with broken
modified super-Schr\"odinger symmetry generators. Furthermore, we find that
eigenmodes form supermultiplets of a modified supersymmetry preserved by the
static BPS backgrounds. As a consequence of the modified supersymmetry,
infinite towers of explicit spectra can be found for eigenmodes correspond- ing
to bosonic and fermionic lowest Landau levels.
