  The aim of this paper is to consider a possibility of constructing for
arbitrary dynamical systems with first-class constraints a generalized
canonical quantization method based on the osp(1,2) supersymmetry principle.
This proposal can be considered as a counterpart to the osp(1,2)-covariant
Lagrangian quantization method introduced recently by Geyer, Lavrov and
M\"ulsch. The gauge dependence of Green's functions is studied. It is shown
that if the parameter m^2 of the osp(1,2) superalgebra is not equal to zero
then the vacuum functional and S-matrix depend on the gauge. In the limit $m\to
0$ the gauge independence of vacuum functional and S - matrix are restored. The
Ward identities related to the osp(1,2) symmetry are derived.
