We study a generic model in which the dark sector is composed of a Majorana dark matter $chi_1$, its excited state $chi_2$, both at the electroweak scale, and a light dark photon $Z$ with $m_{Z} sim 10^{-4}$ eV. The light $Z$ enhances the self-scattering elastic cross section $chi_1 chi_1 to chi_1 chi_1$ enough to solve the small scale problems in the $N$-body simulations with the cold dark matter. The dark matter communicates with the SM via kinetic mixing parameterized by $epsilon$. The inelastic scattering process $chi_1 chi_1 to chi_2 chi_2$ followed by the prompt decay $chi_2 to chi_1 Z$ generates energetic $Z$. By setting $delta equiv m_{chi_2} - m_{chi_1} simeq 2.8$ keV and $epsilon sim 10^{-10}$ the excess in the electron-recoil data at the XENON1T experiment can be explained by the dark photoelectric effect. The relic abundance of the dark matter can also be accommodated by the thermal freeze-out mechanism via the annihilation $chi_1 chi_1 (chi_2 chi_2) to Z Z$ with the dark gauge coupling constant $alpha_X sim 10^{-3}$.
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