A search for exotic dark matter (DM) in the sub-GeV mass range has been conducted using 205 kg day data taken from a p-type point contact germanium detector of the CDEX-10 experiment at China's Jinping underground laboratory. New low-mass dark matter searching channels, neutral current fermionic DM absorption (χ+A→ν+A) and DM-nucleus 3→2 scattering (χ+χ+A→ϕ+A), have been analyzed with an energy threshold of 160 eVee. No significant signal was found; thus new limits on the DM-nucleon interaction cross section are set for both models at the sub-GeV DM mass region. A cross section limit for the fermionic DM absorption is set to be 2.5×10^{-46} cm^{2} (90% C.L.) at DM mass of 10 MeV/c^{2}. For the DM-nucleus 3→2 scattering scenario, limits are extended to DM mass of 5 and 14 MeV/c^{2} for the massless dark photon and bound DM final state, respectively.