  The iron-based superconductor FeSe$_{1-x}$Te$_{x}$ (FST) has recently gained
significant attention as a host of two distinct physical phenomena: ($i$)
Majorana zero modes which can serve as potential topologically protected
qubits, and ($ii$) a realization of the orbital selective Mott transition
(OSMT). In this Letter, we connect these two phenomena and provide new insights
into the interplay between strong electronic correlations and non-trivial
topology in FST. Using linearized quasiparticle self-consistent GW plus
dynamical mean-field theory, we show that the topologically protected Dirac
surface state has substantial Fe($d_{xy}$) character. The proximity to the OSMT
plays a dual role, it facilitates the appearance of the topological surface
state by bringing the Dirac cone close to the chemical potential, but destroys
the Z$_{2}$ topological superconductivity when the system is too close to the
orbital selective Mott phase (OSMP). We derive a reduced effective Hamiltonian
that describes the topological band. Its parameters capture all the chemical
trends found in the first principles calculation. Our findings provide a
framework for further study of the interplay between strong electronic
correlations and non-trivial topology in other iron-based superconductors.
