In this work, the bound state solutions of the deformed Dirac equation (DDE) have been determined with the improved generalized inversely quadratic Yukawa potential including Coulomb-like tensor (IGIQYPCLT) interaction under the condition of spin symmetry and pseudospin symmetry in the deformation Dirac theory (DDT) symmetries for with the arbitrary spin-orbit quantum number k. The IGIQYPCLT interaction includes generalized inversely quadratic Yukawa potential as the main part and other new exponential terms due to the topological properties of deformation space space. The parametric Bopp’s shift method and standard perturbation theory are used to obtain the relativistic and nonrelativistic energy eigenvalues for studied potential. The new values that we get appeared sensitive to the quantum numbers j,k,l,l~,s,s~,m,m~\documentclass[12pt]{minimal}
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\begin{document}$$\left( j,k,l,{\widetilde{l}},s,{\widetilde{s}},m,{\widetilde{m}} \right) $$\end{document}, the mixed potential depths V0,T\documentclass[12pt]{minimal}
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\begin{document}$$\left( V_{0},T\right) $$\end{document}, the range of the potential α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha $$\end{document}, and noncommutativity parameters Θ,σ,χ\documentclass[12pt]{minimal}
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\begin{document}$$\left( \Theta ,\sigma ,\chi \right) $$\end{document}. The energies spectra of the improved Mie-type potential within improved Coulomb-like potential within improved have been derived as particular cases of the IGIQYPCLT model. We have applied our results to obtaining the new nonrelativistic energies that represent the binding energy between the quark and anti-quark to determine the modified spin-averaged mass spectra of heavy and heavy-light mesons HLM such as cc¯\documentclass[12pt]{minimal}
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\begin{document}$$c{\overline{c}}$$\end{document}, bb¯\documentclass[12pt]{minimal}
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\begin{document}$$b{\overline{s}}$$\end{document}, cs¯\documentclass[12pt]{minimal}
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\begin{document}$$c {\overline{s}}$$\end{document}, and bq¯\documentclass[12pt]{minimal}
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\begin{document}$$b{\overline{q}}$$\end{document}, q = (u, d) in both NRQM and ENRQM symmetries. It is worth mentioning that, for all cases, to make the three simultaneous limits Θ,σ,χ→0,0,0\documentclass[12pt]{minimal}
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\begin{document}$$\left( \Theta ,\sigma ,\chi \right) \rightarrow \left( 0,0,0\right) $$\end{document}, the ordinary physical quantities are recovered all known physical values in the framework of relativistic and nonrelativistic quantum mechanics known in the literature.
