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A topological superconductor, characterized by either a chiral order parameter or a topological surface state in proximity to bulk superconductivity, is foundational to topological quantum computing. A key open challenge is whether electron-electron interactions can tune such topological superconducting phase. Here, we provide experimental signatures of a unique topological superconducting phase in competition with electronic correlations in 10-unit-cell thick FeTexSe1-x films grown on SrTiO3 substrates. When the Te content x exceeds 0.7, we observe a topological transition marked by the emergence of a superconducting surface state. Near the FeTe limit, the system undergoes another transition where the surface state disappears, and superconductivity is suppressed. Theory suggests that electron-electron interactions in the odd-parity xy- band drives this second topological transition. The flattening and eventual decoherence of dxy-derived bands track the superconducting dome, linking correlation effects directly to superconducting coherent transport. Our work establishes many-body electronic correlations as a sensitive knob for tuning topology and superconductivity, offering a pathway to engineer new topological phases in correlated materials.