Transport properties of the kesterite-like single crystals of Cu₂ZnSnS₄, Cu₂ZnSn_xGe_1−xSe₄ and Cu₂ZnGeS₄ are investigated in pulsed magnetic fields up to B = 20 T. The Mott variable-range hopping (VRH) conduction is established by investigations of the resistivity, ρ (T), in all the materials mentioned above within broad temperature intervals of ΔT_v4 ∼ 50–150 K, 50–250 K and 100–200 K, respectively. In addition, the Shklovskii-Efros VRH conductivity below T_v2 ∼ 3–4 K, the nearest-neighbour hopping (NNH) charge transfer between T ∼ 250–320 K and the conductivity by activation of holes on the mobility threshold at temperatures outside ΔT_v4, respectively, are observed in these materials. In Cu₂ZnSnS₄, magnetoresistance (MR) contains only a positive contribution, connected mainly to a shrinkage of impurity wave functions by the magnetic field. At the same time, a negative contribution to MR, attributable to interference effects in VRH, is observed in Cu₂ZnSn_xGe_1−xSe₄ and, especially, in Cu₂ZnGeS₄. The joint analysis of the MR and ρ (T) data has yielded important electronic parameters of the materials. This includes widths of the acceptor band W and of the Coulomb gap Δ the NNH activation energy E_n, the localization radius a, the acceptor concentration N_A and the density of the localized states at the Fermi level, g (μ). A dramatic increase of a in Cu₂ZnSnS₄ with decreasing T is observed, whereas in Cu₂ZnSn_xGe_1−xSe₄ all the parameter W, E_n, g (μ), a and N_A are non-monotonic functions of x. Finally, in Cu₂ZnGeS₄ the Hall coefficient R_H (T) is negative (despite of the p-type conduction), exhibiting the dependence close to that of ρ (T) in the Mott VRH interval.