  Light weakly interacting particles could be copiously produced in the Sun
which, as a well-understood star, could provide severe constraints on such new
physics. In this work, we calculate the solar production rates of light gauge
bosons (e.g. dark photon) arising from various $U(1)$ extensions of the
standard model. It is known that the dark photon production rate is suppressed
by the dark photon mass if it is well below the plasmon mass of the medium. We
show that for more general $U(1)$ gauge bosons, this suppression is absent if
the couplings are not in alignment with those of the photon. We investigate a
few frequently discussed $U(1)$ models including $B-L$, $L_{\mu}-L_{\tau}$, and
$L_{e}-L_{\mu(\tau)}$, and derive the stellar cooling bounds for these models.
