  Complex radiative transfer (RT) of the Lyman-$\alpha$ photons poses a
theoretical challenge to galaxy surveys which infer the large-scale structure
with Lyman-$\alpha$ emitters (LAEs). Guided by RT simulations, prior studies
investigated the impact of RT on the large-scale LAE clustering, and claimed
that RT induces a selection effect which results in an anisotropic distortion
even in real space but in an otherwise negligible effect in redshift space.
However, our previous study, which relies on a full radiative transfer code run
on the Illustris simulations, shows that the anisotropic selection effect was
drastically reduced with higher spatial resolution. Adopting the same
simulation framework, we further study the impact of RT on the LAE clustering
in redshift space. Since we measure LAE's radial position through a spectral
peak of a Lyman-$\alpha$ emission, the frequency shift due to RT contaminates
the redshift measurement and hence the inferred radial position in redshift
space. We demonstrate that this additional RT offset suppresses the LAE
clustering along the line of sight, which can be interpreted as a novel
Fingers-of-God (FoG) effect. To assess the FoG effect, we develop a theoretical
framework with particular emphasis on its connection with the underlying
one-point velocity distribution which simultaneously takes into account the RT
offset as well as the peculiar velocity that is commonly studied in the context
of the Redshift Space Distortion (RSD). Although our findings strongly
encourage a more careful RSD modeling in LAE surveys, we also seek a method to
mitigate the additional FoG effect due to RT by making use of other information
in a Lyman-$\alpha$ spectrum.
