We discuss a novel effect in neutrinoless double beta (0{ u}{beta}{beta}) 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 i
mpact of nuclear medium via Lepton Number Violating (LNV) 4-fermion interactions of neutrino with quarks from decaying nucleus. The net effect of these interactions is generation of an effective in-medium Majorana neutrino mass matrix. The enhanced rate of the 0{ u}{beta}{beta}-decay can lead to the apparent incompatibility of observations of the 0{ u}{beta}{beta}-decay with the value of the neutrino mass determined or restricted by the {beta}-decay and cosmological data. The effective neutrino masses and mixing are calculated for the complete set of the relevant 4-fermion neutrino-quark operators. Using experimental data on the 0{ u}{beta}{beta}-decay in combination with the {beta}-decay and cosmological data we evaluate the characteristic scales of the LNV operators: {Lambda} > 2.4 TeV.
