The dark matter fermion production has studied at lepton colliders viaphoton-dark photon-photon exchange, the results show that, the productioncross-section at e e collider is the same as at collider when the initialbeams are unpolarized or both the initial beams are left- or right-polarized. In caseof mix between both the initial beams are left-polarized with both the initial beamsare right-polarized, the cross-section is very much bigger than thee e cross-section, and the cross-section strongly depends on thepolarization of initial beams.