  This Letter presents results of a search for the mixing of a sub-eV sterile
neutrino with three active neutrinos based on the full data sample of the Daya
Bay Reactor Neutrino Experiment, collected during 3158 days of detector
operation, which contains $5.55 \times 10^{6}$ reactor \anue candidates
identified as inverse beta-decay interactions followed by neutron-capture on
gadolinium. The analysis benefits from a doubling of the statistics of our
previous result and from improvements of several important systematic
uncertainties. No significant oscillation due to mixing of a sub-eV sterile
neutrino with active neutrinos was found. Exclusion limits are set by both
Feldman-Cousins and CLs methods. Light sterile neutrino mixing with $\sin^2
2\theta_{14} \gtrsim 0.01$ can be excluded at 95\% confidence level in the
region of $0.01$ eV$^2 \lesssim |\Delta m^{2}_{41}| \lesssim 0.1 $ eV$^2$. This
result represents the world-leading constraints in the region of $2 \times
10^{-4}$ eV$^2 \lesssim |\Delta m^{2}_{41}| \lesssim 0.2 $ eV$^2$.
