  We consider an SU(3)'_c\times SU(2)'_L\times U(1)'_Y mirror sector where the
field content and dimensionless couplings are a copy of the SU(3)_c\times
SU(2)_L\times U(1)_Y ordinary sector. Our model also contains three
gauge-singlet fermions with heavy Majorana masses and an [SU(2)_L\times
SU(2)'_L]-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 SU(2)'_L 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
[SU(2)'_L]-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.
