  LHAASO J0621$+$3755 is a TeV gamma-ray halo newly identified by LHAASO-KM2A.
It is likely to be generated by electrons trapped in a slow-diffusion zone
around PSR J0622$+$3749 through inverse Compton scattering. When the gamma-ray
spectrum of LHAASO-KM2A is fitted, the GeV fluxes derived by the commonly used
one-zone normal diffusion model for electron propagation are significantly
higher than the upper limits (ULs) of Fermi-LAT. In this work, we respectively
adopt the one-zone superdiffusion and two-zone normal diffusion models to solve
this conflict. For the superdiffusion scenario, we find that a model with
superdiffusion index $\alpha\lesssim1.2$ can meet the constraints of Fermi-LAT
observation. For the two-zone diffusion scenario, the size of the
slow-diffusion zone is required to be smaller than $\sim50$ pc, which is
consistent with theoretical expectations. Future precise measurements of the
Geminga halo may further distinguish between these two scenarios for the
electron propagation in pulsar halos.

High Energy Astrophysical Phenomena;High Energy Physics - Phenomenology