We present our investigations on the superconducting properties of monolayers of FeSe$_{0.5}$Te$_{0.5}$ grown on the 3D topological insulator Bi$_{2}$Se$_{1.2}$Te$_{1.8}$ using low temperature scanning tunneling spectroscopy (STS). While the morphology and the overall transition temperature resemble those of similarly doped bulk crystals, the spatially resolved spectroscopic data at 1.1K shows a much larger spatial inhomogeneity in the superconducting energy gaps. Despite the gap inhomogeneity all the spectra can be fitted with a two-fold anisotropic s-wave gap function. The two-fold nature of the gap symmetry is evident from the Bogoliubov quasiparticle interference (QPI) pattern which shows distinct C$_{2}$ symmetric scattering intensities. We argue that the gap inhomogeneity emerges as a result of intrinsic disorder in our system similar to disordered conventional superconductors. Even though most of our findings clearly differ from the current understanding of the corresponding bulk system, it provides an ideal platform to study unconventional superconductivity in Fe chalcogenides thinned down to a single layer and in close proximity to a topological insulator.
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