  The non-Hermitian skin effect (NHSE) is a fascinating phenomenon in
nonequilibrium systems where eigenstates massively localize at the systems'
boundaries, pumping (quasi-)particles loaded in these systems unidirectionally
to the boundaries. Its interplay with many-body effects have been vigorously
studied recently, and inter-particle repulsion or Fermi degeneracy pressure
have been shown to limit the boundary accumulation induced by the NHSE both in
their eigensolutions and dynamics. However, in this work we found that anyonic
statistics can even more profoundly affect the NHSE dynamics, suppressing or
even reversing the state dynamicss against the localizing direction of the
NHSE. This phenomenon is found to be more pronounced when more particles are
involved.The spreading of quantum information in this system shows even more
exotic phenomena, where NHSE affects only the information dynamics for a
thermal ensemble, but not that for a single initial state. Our results open up
a new avenue on exploring novel non-Hermitian phenomena arisen from the
interplay between NHSE and anyonic statistics, and can potentially be
demonstrated in ultracold atomic quantum simulators and quantum computers.
