  We show that a (2+1)-dimensional $P,T-$invariant free fermion system,
relevant to $P,T-$conserving models of high-$T_c$ superconductivity, has a
U(1,1) dynamical symmetry as well as an $N=3$ supersymmetry with the even
generator being a quadratic function of the spin operator and of the generator
of chiral ${\rm U_c(1)}$ transformations. We demonstrate that the hidden
supersymmetry leads to a non-standard superextension of the (2+1)-dimensional
Poincar\'e group. As a result, the one particle states of the $P,T-$invariant
fermion system realize an irreducible representation of the Poincar\'e
supergroup labelled by the zero eigenvalue of the superspin operator.
