  In this article, the mass spectra of mesons with one or two heavy quarks and
their diquarks partners are estimated within a non-relativistic framework by
solving Schr\"odinger equation with an effective potential inspired by a
symmetry preserving Poincar\'e covariant vector-vector contact interaction
model of quantum chromodynamics. Matrix Numerov method is implemented for this
purpose. In our survey of mesons with heavy quarks, we fix the model parameter
to the masses of ground-states and then extend our calculations for radial
excitations and diquarks. The potential model used in this work gives results
which are in good agreement with experimental data and other theoretical
calculations.
