  We consider a generalization of the abelian Higgs model with a Chern-Simons
term by modifying two terms of the usual Lagrangian. We multiply a dielectric
function with the Maxwell kinetic energy term and incorporate nonminimal
interaction by considering generalized covariant derivative. We show that for a
particular choice of the dielectric function this model admits topological
vortices satisfying Bogomol'nyi bound for which the magnetic flux is not
quantized even though the energy is quantized. Furthermore, the vortex solution
in each topological sector is infinitely degenerate.
