  We have studied BPS vortices in a CPT-odd and Lorentz-violating
Maxwell-Chern-Simons-Higgs (MCSH) electrodynamics attained from the dimensional
reduction of the Carroll-Field-Jackiw-Higgs model. The Lorentz-violating
parameter induces a pronounced behavior at origin (for the magnetic/electric
fields and energy density) which is absent in the MCSH vortices. For some
combination of the Lorentz-violating coefficients there always exist a
sufficiently large winding number $n_{0}$ such that for all $% |n|\geq |n_{0}|$
the magnetic field flips its signal, yielding two well defined regions with
opposite magnetic flux. However, the total magnetic flux remains quantized and
proportional to the winding number.
