  Using Schr\"{o}dinger's formalism, we investigate the quantum eigenstates of
the heavy mesons trapped by a point-like defect and by Cornell's potential. One
implements this defect to the model considering a spherical metric profile
coupled to it. Furthermore, the Nikiforov-Uvarov method is applied to theory to
study the quantum eigenstates of the heavy mesons. To calculate the quantum
information entropy (QIE), one considers the wave functions that describe the
charmonium and bottomonium states. To explore the QIE, we use the well-known
Shannon's entropy formulated at the position and reciprocal space. The analysis
of the QIE gives us relevant information about how the quantum information
change with the variation of the point-like defect. Consequently, considering
the Bialynicki-Birula and Mycielski (BBM) relation, we show how this defect
influences the quarkonium position and momentum uncertainty measures.
