Activated resistivity, ρ(T), and positive magnetoresistance (MR) are observed in Cu₂ZnSnS₄ single crystals within the temperature interval between T ∼ 2 and 300 K in pulsed magnetic fields of B up to 20 T. Between T ∼ 50 and 150 K, the charge transfer is described by the Mott variable-range hopping (VRH) transport over localized states of the defect acceptor band with width W ∼ 12-25 meV. Up to the highest applied fields, MR follows the law ln ρ(B) ∞ B² pertinent to the VRH conduction at λ ≫ a, where λ is the magnetic length and a is the localization radius. The joint analysis of the MR and ρ(T) data yielded a series of microscopic parameters, including the values of a 22-45 Å, depending on the proximity of a sample to the metal-insulator transition. However, below T ∼ 3-4 K the Shklovskii-Efros VRH conduction is observed. Here, the behavior of MR changes drastically, exhibiting a sharp contraction of the quadratic MR region and transformation of the MR law into those of ln ρ (B) ∞ B^2/3 or ∞ B^3/4 when B is increased. In addition, such behavior of MR is accompanied by a dramatic increase of the localization radius a ≈ 50-170 Å. Both anomalies above are explained quantitatively by the same reason, connected to the constructive interference of different paths arising from multiple scattering of hopping carriers at low temperatures. In particular, the low-temperature values of the localization radius, evaluated in frames of the theory of interference phenomena in the VRH conduction, exhibit a reasonable agreement with the experimental data.