We present the first results of the search for sub-MeV fermionic dark matter absorbed by electron targets of Germanium using the 205.4~kg·day data collected by the CDEX-10 experiment, with the analysis threshold of 160~eVee. No significant dark matter (DM) signals over the background are observed. Results are presented as limits on the cross section of DM--electron interaction. We present new constraints of cross section in the DM range of 0.1--10 keV/c² for vector and axial-vector interaction. The upper limit on the cross section is set to be 5.5×10⁻⁴⁶~cm² for vector interaction, and 1.8×10⁻⁴⁶~cm² for axial-vector interaction at DM mass of 5 keV/c².
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