KeV Scale Frozen-in Self-Interacting Fermionic Dark Matter

We present a model in which the dark matter particle is frozen-in at MeV scale. In this model, the mediator between the standard model sector and the dark sector can automatically provide a self-interaction for dark matter. The interaction strength is naturally to be the in the region in favor of the cluster mass deficit anomaly. Due to the self-scattering, the Lyman-$\alpha$ constraint can be relaxed to $m_D \gtrsim 2 $ keV. In this region the self-interaction and the Fermi pressure both play roles on forming a dark matter core at the center of the dwarf galaxies.