  We construct d=1 sigma models of the Wess-Zumino type on the SU(n|1)/U(n)
fermionic cosets. Such models can be regarded as a particular supersymmetric
extension (with a target space supersymmetry) of the classical Landau model,
when a charged particle possesses only fermionic coordinates. We consider both
classical and quantum models, and prove the unitarity of the quantum model by
introducing the metric operator on the Hilbert space of the quantum states,
such that all their norms become positive-definite. It is remarkable that the
quantum n=2 model exhibits hidden SU(2|2) symmetry. We also discuss the planar
limit of these models. The Hilbert space in the planar n=2 case is shown to
carry SU(2|2) symmetry which is different from that of the SU(2|1)/U(1) model.
