  The inelastic dark matter model is one kind of popular models for the light
dark matter (DM) below $O(1)$ GeV. If the mass splitting between DM excited and
ground states is small enough, the co-annihilation becomes the dominant channel
for thermal relic density and the DM excited state can be long-lived at the
collider scale. We study scalar and fermion inelastic dark matter models for $
{\cal O}(1) $ GeV DM at Belle II with $ U(1)_D $ dark gauge symmetry broken
into its $Z_2$ subgroup. We focus on dilepton displaced vertex signatures from
decays of the DM excited state. With the help of precise displaced vertex
detection ability at Belle II, we can explore the DM spin, mass and mass
splitting between DM excited and ground states. Especially, we show scalar and
fermion DM candidates can be discriminated and the mass and mass splitting of
DM sector can be determined within the percentage of deviation for some
benchmark points. Furthermore, the allowed parameter space to explain the
excess of muon $(g-2)_\mu$ is also studied and it can be covered in our
displaced vertex analysis during the early stage of Belle II experiment.
