We report on a study of the superconducting order parameter in Fe(Te$_{1-x}$Se$_{x}$) thin films (with different Se contents: x=0.3, 0.4, 0.5) by means of point-contact Andreev-reflection spectroscopy (PCARS). The PCARS spectra show reproducible evidence of multiple structures, namely two clear conductance maxima associated to a superconducting gap of amplitude $Delta_E simeq 2.75 k_B T_c$ and additional shoulders at higher energy that, as we show, are the signature of the strong interaction of charge carriers with a bosonic mode whose characteristic energy coincides with the spin-resonance energy. The details of some PCARS spectra at low energy suggest the presence of a smaller and not easily discernible gap of amplitude $Delta_H simeq 1.75 k_B T_c$. The existence of this gap and its amplitude are confirmed by PCARS measurements in Fe(Te$_{1-x}$Se$_{x}$) single crystals. The values of the two gaps $Delta_E$ and $Delta_H$, once plotted as a function of the local critical temperature $T_c^A$, turn out to be in perfect agreement with the results obtained by various experimental techniques reported in literature.
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