Electron-nuclear quadrupole interaction in trimeric antiferromagnetic clusters with half-integer ion spins is considered. The electronic shell of the exchange cluster is shown to produce electric field gradient at the nuclei. The antisymmetric exchange interaction of Dzialoshinskii leads to the flattening of the electric field gradient at the nuclei, located in geometrically non-equivalent positions due to distortions. The parameters of the quadrupole hamiltonian depend upon the external magnetic field. The magnetic field, parallel to the plane of the cluster, reduces the antisymmetric exchange interaction and re-establishes the geometric non-equivalence of the ions. The hyperfine fields on Mössbauer nuclei is examined. Non-collinear spin structure of the trimeric cluster is predicted. The theory explains qualitatively the peculiarities of Mössbauer spectra of iron three-nuclear carboxylate crystals.