Active Galactic Nucleus (AGN) variability can be used to study the physics of the region in the vicinity of the central black hole. In this paper, we investigated intra-night optical variability of AGN in the COSMOS field in order to understand the AGN instability at the smallest scale. Observations were performed using the KMTNet on three separate nights for 2.5-5 hour at a cadence of 20-30 min. We find that the observation enables the detection of the short-term variability as small as $sim$ 0.02 and 0.1 mag for $R sim$ 18 and 20 mag sources, respectively. Using four selection methods (X-rays, mid-infrared, radio, and matching with SDSS quasars), 394 AGNs are detected in the 4 deg$^2$ field of view. After differential photometry and $chi^2-$test, we classify intra-night variable AGNs. But the fraction of variable AGNs (0-8 %) is consistent with a statistical fluctuation from null result. Eight out of 394 AGNs are found to be intra-night variable in two filters or two nights with a variability level of 0.1 mag, suggesting that they are strong candidates for intra-night variable AGNs. Still they represent a small population (2 %). There is no sub-category of AGNs that shows a statistically significant intra-night variability.
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