Observations of tailward cold O+ beams (COBs) in the distant lobe/mantle shed new light upon plasma supply mechanisms to the magnetotail since their location up to a tailward distance of 210 RE is not explicable with a conventional view of magnetospheric dynamics. The COBs exist primarily in the mantlelike regions that correspond to the transport route of magnetic flux tubes reconnected at the dayside magnetopause, and thus it has been suggested that these high-energy COBs in the distant lobe/mantle have originated from trapped O+ ions in the dayside magnetosphere. In order to examine the validity of this scenario the phase space density (PSD) of the COBs observed by Geotail is compared statistically with that of mirroring O+ ions around the cusp observed by FAST at low altitudes (400--4200 km) utilizing particle trajectory tracings in empirical magnetospheric models. The energy distribution of the averaged peak PSD of COBs is different at energies below and above ~1 keV and thus suggests that more than one source contributes to the COBs. The mirroring O+ increases in quantity with increasing solar activity and suggest increment of trapped O+ ions in the dayside magnetosphere. A statistical comparison shows that the O+ PSD around the low-altitude cusp is similar to that of COBs above ~1 keV, while the COB PSD is typically higher than that of O+ at FAST at energies <~1 keV. These results suggest that the trapped O+ in the dayside magnetosphere is a potential source of COBs at energies above 1 keV, while for COBs below 1 keV, polar O+ outflows from the cusp/cleft regions are the most probable source, as suggested by a conventional view.