Electron-phonon coupling (EPC) plays an important role in FeSe, yet theoretical predictions have struggled to reconcile with experiments on doping- and pressure-dependent superconductivity. Here, we employ dynamical mean-field theory to investigate correlation-corrected EPC in FeSe under carrier doping and pressure. By incorporating correlation-corrected EPC strength and applying the Migdal-Eliashberg formalism for phonon-mediated superconductivity, we predict superconducting transition temperatures $T_c$ that closely match experiments and reproduce the observed doping- and pressure-dependent trends. We further find that the electronic correlation strength, characterized by the bandwidth near the Fermi level, shows an opposite trend to $T_c$, in contrast to EPC. Our work demonstrates the consistency of the correlation-promoted EPC and $T_c$ over a range of experimental conditions, which suggests that superconductivity in FeSe may originate primarily from correlation-promoted electron-phonon coupling.

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• Electron-phonon coupling
• Iron-based superconductors
• Unconventional superconductors
• Dynamical mean field theory
• Electron-correlation calculations