  Abelian dark sector scenarios embedded into the two-Higgs doublet model are
scrutinized within the Coherent Elastic Neutrino-Nucleus Scattering (CE$\nu$NS)
experiment, which was first measured by the COHERENT Collaboration in 2017 with
an ongoing effort to improve it since then and recently released data for the
CsI target in 2022. In the theoretical framework, it is assumed that there is a
$U(1)$ gauge group in the dark sector with a non-zero kinetic mixing with the
hypercharge field. The COHERENT data for the targets CsI and liquid argon (LAr)
are treated in both single and multi bin bases to constrain the multi
dimensional parameter space, spanned by the dark gauge coupling, kinetic mixing
parameter and the dark photon mass, of totally seven different representative
scenarios which are also compared and contrasted among each other to find out
about the most sensitive one to the data. The effect of refined quenching
factor is also addressed.
