  Red dwarfs have been suggested to be among the possible astrophysical species
accelerating particles and emitting TeV $\gamma$-rays. As an effort to search
for the GeV $\gamma$-ray counterparts of the suggested TeV emission from eight
red dwarfs, we analyse the 0.2--500 GeV $\gamma$-ray emission of the regions
covering them exploiting the $\sim$13.6 yr Pass 8 data of the Fermi Large Area
Telescope. A GeV $\gamma$-ray emission excess with significance of 3.8$\sigma$
is detected in the direction of the red dwarf V962 Tau. This emission contains
V962 Tau in 1$\sigma$ error radius and is independent of the catalog source.
However, the stellar flare scenario can hardly explain the total energy and
lightcurve derived from the $\gamma$-ray emission in view of the spectral
analysis. We also analyse the lightcurves in the positions of the eight red
dwarfs and no time bin with significance $>$5$\sigma$ is found. Therefore, no
significant emission from the red dwarfs could be concluded to be detected by
Fermi-LAT.
