In this work, we present two gauge models for light-dark matter: one with an exotic positive charged lepton and the other one is a variant with right-handed neutrinos. The scalar self-interacting dark matters are stable without imposing new symmetry and should be weak-interacting. We study the impact of the self-interacting light dark matter on the formation of the dark halo, the observation properties of neutron stars, and its effect on the gravitational wave signal. We also present a search by the LIGO-Virgo-KAGRA collaborations for ultralight dark matter using cross-correlation and excess power methods for O3 observing run.