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We consider a gauged $U(1)_x$ extension of the standard model and of theminimal supersymmetric standard model where the dark matter fields are chargedunder $U(1)_x$ and carry lepton number while the standard model fields andfields of the minimal supersymmetric standard model are neutral under $U(1)_x$.We consider leptogenesis in this class of models with all fundamentalinteractions having no violation of lepton number, and the total $B-L$ in theuniverse vanishes. Such leptogenesis leads to equal and opposite lepton numbersin the visible sector and in the dark sector, and thus also produces asymmetricdark matter. Part of the lepton numbers generated in the leptonic sectorsubsequently transfer to the baryonic sector via sphaleron interactions. Thestability of the dark particles is protected by the $U(1)_x$ gauge symmetry. Akinetic mixing between the $U(1)_x$ and the $U(1)_Y$ gauge bosons allows fordissipation of the symmetric component of dark matter. The case when $U(1)_x$is $U(1)_{B-L}$ is also discussed for the supersymmetric case. This case isparticularly interesting in that we have a gauged $U(1)_{B-L}$ which ensuresthe conservation of $B-L$ with an initial condition of a vanishing $B-L$ in theuniverse. Phenomenological implications of the proposed extensions arediscussed, which include implications for electroweak physics, neutrino massesand mixings, and lepton flavor changing processes such as $\ell_i \to \ell_j\gamma$. We also briefly discuss the direct detection of the dark matter in themodel.

Cogenesis in a universe with vanishing $B-L$ within a gauged $U(1)_x$ extension