  Drawing an analogy with the Dirac theory of fermions interacting with
electromagnetic and gravitational field we write down supersymmetric equations
of motion and construct a superfield action for particles with spin 1/4 and 3/4
(quartions), where the role of quartion momentum in effective
(2+1)--dimensional space-time is played by an abelian gauge superfield
propagating in a basic two-dimensional Grassmann-odd space with a cosmological
constant showing itself as the quartion mass. So, the (0|2) (0 even and 2 odd)
dimensional model of quartions interacting with the gauge and gravitational
field manifests itself as an effective (2+1)-dimensional supersymmetric theory
of free quartions.
