  Fermion propagator of the Schwinger Model is revisited from the point of view
of its infrared behavior. The values of anomalous dimensions are found in
arbitrary covariant gauge and in all contributing instanton sectors. In the
case of a gauge invariant, but path dependent propagator, the exponential
dependence, instead of power law one, is established for the special case when
the path is a straight line. The leading behavior is almost identical in any
sector, differing only by the slowly varying, algebraic prefactors. The other
kind of the gauge invariant function, which is the amplitude of the dressed
Dirac fermions, may be reduced, by the appropriate choice of the dressing, to
the gauge variant one, if Landau gauge is imposed.
