  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
$\alpha_X \sim 10^{-3}$.
