We consider an mirror sector where the field content and dimensionless couplings are a copy of the SU(3)c×SU(2)L×U(1)Y ordinary sector. Our model also contains three gauge-singlet fermions with heavy Majorana masses and an -bidoublet Higgs scalar with seesaw-suppressed vacuum expectation value. The mirror sterile neutrino masses will have a form of canonical seesaw while the ordinary active neutrino masses will have a form of double and linear seesaw. In this canonical and double-linear seesaw scenario, we can expect one sterile neutrino at the eV scale and the other two above the MeV scale to fit the cosmological and short baseline neutrino oscillation data. Associated with the SU(2)L and sphaleron processes, the decays of the fermion singlets can simultaneously generate a lepton asymmetry in the [SU(2)L]-doublet leptons and an equal lepton asymmetry in the -doublet leptons to explain the existence of baryonic and dark matter. The lightest mirror baryon then should have a determined mass around 5 GeV to account for the dark matter relic density. The U(1) kinetic mixing can open a window for dark matter direct detection.