  We have studied the existence de self-dual solitons in a gauged version of
the baby Skyrme model in which the gauge field dynamics is governed by the
Maxwell-Chern-Simons action. For such a purpose, we have developed a detailed
implementation of the Bogomol'nyi-Prasad-Sommerfield formalism providing the
self-dual equations whose solutions saturate the energy lower bound. Such a
bound related to the topological charge of the Skyrme field becomes quantized
whereas both the total magnetic flux and the total electrical charge are not.
We have found two types of self-dual Skyrme field profiles: the first is
described by a solution which decays following an exponential-law ($e^{-\alpha
r^2}$, $\alpha>0$); the second is portrayed by a solution having a power-law
decay ($r^{-\beta}$, $\beta>0$). On other hand, in both cases the asymptotic
behavior of the gauge field is similar to the one presented in the context of
the Abelian Higgs models describing Abrikosov-Nielsen-Olesen charged vortices.
Other interesting feature we highlight is the localized magnetic flux
inversion, a property does not observed in others gauged baby Skyrme models
already studied in literature. Numerical results are presented for rotationally
symmetrical field configurations by remarking some of its essential features.
