  We start from a Lorentz non-invariant Abelian-Higgs model in 1+3 dimensions,
and carry out its dimensional reduction to $D=1+2$. The planar model resulting
thereof is composed by a Maxwell-Chern-Simons-Proca gauge sector, a massive
scalar sector, and a mixing term (involving the fixed background, $v^{\mu}$)
that realizes Lorentz violation for the reduced model. Vortex-type solutions of
the planar model are investigated,revealing charged vortex configurations that
recover the usual Nielsen-Olesen configuration in the asymptotic regime. The
Aharonov-Casher Effect in layered superconductors, that shows interference of
neutral particles with a magnetic moment moving around a line charge, is also
studied. Our charged vortex solutions exhibit a screened electric field that
induces the same phase shift as the one caused by the charged wire.
