  We investigate the arising of an analogue of the Landau quantization from a
background of the violation of the Lorentz symmetry established by a time-like
4-vector and a field configuration of crossed electric and magnetic field. We
also analyse the effects on this Landau-type system subject to a hard-wall
confining potential by showing a particular case where a discrete spectrum of
energy can be obtained. Further, we analyse the effects of a linear confining
potential on the Landau-type system. We show that a quantum effect
characterized by the dependence of the cyclotron frequency on the quantum
numbers of the system can arise in this analogue of the Landau system. As an
example, we calculate the cyclotron frequency associated with ground state of
the system.
