  We study a sample of 14 spectroscopically confirmed Ly$\alpha$ Emitters
(LAEs) in the late era of reionization (at redshift $z\approx6$) based on the
JWST/NIRCam imaging dataset. These LAEs with high Ly$\alpha$ luminosity of
$L$(Ly$\alpha$) $\sim10^{42.4-43.4}$ erg s$^{-1}$ have been covered by the
(ongoing) COSMOS-Web survey (Kartaltepe et al. 2021; Casey et al. 2022) over
$0.28$ deg$^2$ in four NIRCam bands (F115W, F150W, F277W, and F444W). With JWST
imaging, we determine the UV continua with $M_{\rm UV}$ ranging from ${-}20.5$
to ${-}18.5$ mag. The UV slopes have a median value of $\beta \approx-2.35$,
and the steepest slope can reach $\beta<-3$. Under an excellent spatial
resolution of JWST, we identify three out of the sample as potential
merging/interacting systems. The 14 LAEs (and their components) are compact in
morphology residing substantially below the mass-size relation of high-$z$
galaxies. We further investigate the stellar mass ($M_*$) and star-formation
rates (SFRs). Most of the LAEs lie on the SFR-$M_*$ main-sequence relation
while two of them featured as "little red dots" likely host active galactic
nuclei (AGN), implying a ${\sim}10\%$ AGN fraction. Moreover, we reveal that a
new correlation may exist between Ly$\alpha$ equivalent width and the offset
between Ly$\alpha$ and UV emission ($\Delta d_{\rm Ly\alpha}$) with a median
$\Delta d_{\rm Ly\alpha} \sim 1$ kpc. This could be explained by Ly$\alpha$
radiative transfer process in both ISM and CGM. The results usher a new era of
detailed analysis on high-$z$ LAEs with the JWST capability.
