  We consider the gauged model of Siegel type chiral boson with a Lorentz
non-covariant mass-like term for the gauge fields which is found to be
equivalent to the chiral Schwinger model with Faddeevian anomaly when it is
described in terms of Floreanini-Jackiw type chiral boson. We carry out the
quantization of gauge non-invariant version this model in both the Lagrangian
and Hamiltonian formulation. The quantization of the gauge-invariant version of
this model in the extended phase space also has been carried out in the
Lagrangian formulation. The gauge-invariant version of this model in the
extended phase space is found to map onto the physical phase space with the
appropriate gauge fixing condition. BRST symmetry associated with this model
has been studied with different gauge fixing terms. It has been shown that the
same model shows off-shell as well as on-shell BRST invariance depending on the
choice of gauge fixing term.
