This study investigates the probable heavy-cluster radioactivity from superheavy nuclei with 100 < Z <120 using the modified double-folding formalism by applying the Pauli exclusion principle. To this aim, the half-lives of the most probable cluster radioactivity are investigated by applying the Pauli exclusion principle to the internal energy of the dinuclear system. The results indicated that considering Pauli blocking as a modification term in calculating the double-folding potential leads to more consistent half-lives with the predictions of other theoretical models. Also, the competition between α decay and heavy-cluster radioactivity at the superheavy region is investigated. The obtained results show that the cluster radioactivity can be expected for some superheavy nuclei with Z = 120.