The planar Dirac and the topologically massive vector gauge fields are unified into a supermultiplet involving no auxiliary fields. The super-Poincaré symmetry emerges from the osp(1∣2) supersymmetry realized in terms of the deformed Heisenberg algebra underlying the construction. The nonrelativistic limit yields spin 1/2 as well as new, spin 1 “Lévy–Leblond-type” equations which, together, carry an N=2 super-Schrödinger symmetry. Part of the latter has its origin in the universal enveloping algebra of the super-Poincaré algebra.