Aimed at the detection of cosmological gas being accreted onto galaxies in the local universe, we examined the Hα emission in the halo of 164 galaxies in the field of view of the Multi-Unit Spectroscopic Explorer Wide survey (MUSE-Wide) with observable Hα (redshift <0.42). An exhaustive screening of the corresponding Hα images led us to select 118 reliable Hα emitting gas clouds. The signals are faint, with a surface brightness of ${10}^{-17.3\pm 0.3}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}\,{\mathrm{arcsec}}^{-2}$ . Through statistical tests and other arguments, we ruled out that they are created by instrumental artifacts, telluric line residuals, or high-redshift interlopers. Around 38% of the time, the Hα line profile shows a double peak with the drop in intensity at the rest frame of the central galaxy, and with a typical peak-to-peak separation of the order of ±200 km s-1. Most line emission clumps are spatially unresolved. The mass of emitting gas is estimated to be between 1 and 10-3 times the stellar mass of the central galaxy. The signals are not isotropically distributed; their azimuth tends to be aligned with the major axis of the corresponding galaxy. The distances to the central galaxies are not random either. The counts drop at a distance >50 galaxy radii, which roughly corresponds to the virial radius of the central galaxy. We explore several physical scenarios to explain this Hα emission, among which accretion disks around rogue intermediate-mass black holes fit the observations best.