The study of hyperfine interaction by high-resolution inelastic neutron scattering is not very well known compared to the other competing techniques viz. nuclear magnetic resonance, Mössbauer, perturbed angular correlation spectroscopy, etc. Also, studies have been limited mostly to magnetically ordered systems. Here, we report such a study on Sr2-xLaxFeCoO6 (x=0,1,2) of which the first (Sr2FeCoO6 with x=0) has a canonical spin-glass state, the second (SrLaFeCoO6 with x=1) has a so-called magnetic glass state, and the third (La2FeCoO6 with x=2) has a magnetically ordered ground state. Our present study revealed a clear inelastic signal for SrLaFeCoO6, a possible inelastic signal for Sr2FeCoO6 below the spin freezing temperatures Tsf, but no inelastic signal at all for the magnetically ordered La2FeCoO6 in the neutron-scattering spectra. The broadened inelastic signals observed suggest hyperfine field distributions in the two disordered magnetic glassy systems, whereas the absent inelastic signal for the third compound suggests no, or a very small, hyperfine field at the Co nucleus due to Co electronic moment. The hyperfine splitting on the Co nucleus is induced by the electronic spin state of the magnetic sample atom, and our experiments add information concerning the timescale of electronic spin fluctuations by the appearance of quasielastic broadening in the μeV range at low Q and spin freezing on the nanosecond timescale below Tsf. Whereas these features are observed at low Q for x=0 and 1, they are absent for La2FeCoO6, which evidences a gradual increase of the elastic intensity only at large Q near an emerging Bragg peak. Thus both electronic magnetic spin freezing and inelastic excitations arising from nuclear hyperfine splitting at the Co site consistently indicate a different behavior for x=2. © 2018 American Physical Society.