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The X-ray, Ultraviolet, Optical emission from radio-quiet AGNs, black hole binaries, and other compact sources, in general, follow a lognormal flux distribution, a linear rms-flux relation, and a (broken) power-law power spectral densities (PSDs). These characteristics are normally attributed to the multiplicative combination of fluctuations in the accretion disk. Similar features have been inferred for some well-observed blazars in different energy bands, but a systematic study over a long duration is still missing. Using a continuous gamma-ray light curves over 3-days cadence from August 2008 - October 2015, we present the first systematic study of these features in four sources: the FR I radio galaxy NGC 1275 and three blazars- Mrk 421, B2 1520+31 and PKS 1510-089. For all, except Mrk 421, the flux spans $\gtrsim$ 2 orders of magnitude. For blazars, a log-normal profile describes the flux histograms better compared to a Gaussian, while none is favored for NGC 1275, the only non-blazar source, suggesting a complex distribution. Regardless of flux histogram profile, the rms-flux relation is linear for all with PSDs being consistent with a power-law shot noise spectrum despite hints of breaks. The inferred results are consistent with the properties of unresolved magnetic reconnection sites, as inferred in the X-ray emission from the whole Solar disk and the statistical characteristics of magnetic reconnection based minijets-in-a-jet model. The results, thus, suggest a strong jet-accretion-disk coupling with energy input from the central source being distributed over a wide range in time and energy by the reconnection process depending on the geometry and local physical conditions.