We discuss a novel effect in neutrinoless double-β (0νββ) decay related with the fact that its underlying mechanisms take place in the nuclear matter environment.We study the neutrino exchange mechanism and demonstrate the possible impact of nuclear medium via lepton-number-violating (LNV) four-fermion interactions of neutrinos with quarks from a decaying nucleus. The net effect of these interactions is the generation of an effective in-medium Majorana neutrino mass matrix. The enhanced rate of the 0νββ decay can lead to the apparent incompatibility of observations of the 0νββ decay with the value of the neutrino mass determined or restricted by the β-decay and cosmological data. The effective neutrino masses and mixing are calculated for the complete set of the relevant four-fermion neutrino-quark operators. Using experimental data on the 0νββ decay in combination with the β-decay and cosmological data, we evaluate the characteristic scales of these operators: Λ_LNV ≥ 2.4 TeV.