  Resonant Inelastic X-Ray Scattering (RIXS) experiments on the iron-based
ladder BaFe$_2$Se$_3$ unveiled an unexpected two-peak structure associated with
local orbital ($dd$) excitations in a block-type antiferromagnetic phase. A
mixed character between correlated band-like and localized excitations was also
reported. Here, we use the density matrix renormalization group method to
calculate the momentum-resolved charge- and orbital-dynamical response
functions of a multi-orbital Hubbard chain. Remarkably, our results
qualitatively resemble the BaFe$_2$Se$_3$ RIXS data, while also capturing the
presence of long-range magnetic order as found in neutron scattering, $only$
when the model is in an exotic orbital-selective Mott phase (OSMP). In the
calculations, the experimentally observed zero-momentum transfer RIXS peaks
correspond to excitations between itinerant and Mott insulating orbitals. We
provide experimentally testable predictions for the momentum-resolved charge
and orbital dynamical structures, which can provide further insight into the
OSMP regime of BaFe$_2$Se$_3$.
