Abstract A systematic search for cyclical sources of γ-ray emission on the period range from days to years in the Fermi-LAT sky is performed. Looking for cyclical emission, the sky is binned into equal-area pixels and the generalized Lomb–Scargle periodogram is computed for each of these pixels. The search on the period range between 2.5 and 30 d in the Galactic plane confirms periodicities of three binaries, LSI +61°303, LS 5039 and 1FGL J1018.6−5856. The all-sky search on the period range between 30 d and 2.5 yr confirm quasi-periodicities of three blazars, PG 1553+113, PKS 2155−304 and BL Lacertae. Evidence for quasi-periodic behaviours of four blazars, 4C +01.28, S5 0716+71, PKS 0805−07 and PKS 2052−47, is presented. Three of these blazars, 4C +01.28, PKS 0805−07 and PKS 2052−47, are located at high redshifts. These three sources are potential candidates to binary systems of supermassive black holes, provided that major galaxy mergers are more frequent and that galaxies are more gas-rich at high redshifts.