Due to their excellent magnetic properties, amorphous metallic alloys (AMAs) are considered for the construction of magnetic cores of radio-frequency cavities in accelerators. Here, they might be exposed to ion bombardment. The influence of irradiation by both light and heavy ions featuring low and high energies, respectively, is followed by the techniques of 57Fe Mössbauer spectrometry. Modifications of surface layers in selected Fe-containing AMAs after ion irradiation are unveiled by detection of conversion electrons and photons of characteristic radiation whereas those in their bulk are derived from standard transmission spectra. Rearrangement of microstructure which favors the formation of magnetically active regions, is observed in surface regions bombarded by light ions. Heavy ions caused pronounced effects in the orientation of net magnetization of the irradiated samples. No measurable impact upon short-range order arrangement was observed. Part I of this paper is devoted to radiation effects in Fe-based AMAs induced by neutron irradiation.