The three-dimensional non-anticommutative superspace

We propose two alternative formulations for a three-dimensional non-anticommutative superspace in which some of the fermionic coordinates obey Clifford anticommutation relations. For this superspace, we construct the supersymmetry generators satisfying standard anticommutation relations and the corresponding supercovariant derivatives. We formulate a scalar superfield theory in such a superspace and calculate its propagator. We also suggest a prescription for the introduction of interactions in such theories.