The main aim of this work is devoted to studying the existence of compact spherical systems representing anisotropic matter distributions within the scenario of alternative theories of gravitation, specifically f(R, T) gravity theory. Besides, a noteworthy and achievable choice on the formulation of f(R, T) gravity is made. To provide the complete set of field equations for the anisotropic matter distribution, it is considered that the functional form of f(R, T) as f(R,T)=R+2χT\documentclass[12pt]{minimal}
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\begin{document}$$f(R, T)=R+2\chi T$$\end{document}, where R and T correspond to scalar curvature and trace of the stress–energy tensor, respectively. Following the embedding class one approach employing the Eisland condition to get a full space–time portrayal interior the astrophysical structure. When the space–time geometry is identified, we construct a suitable anisotropic model by using a new gravitational potential grr\documentclass[12pt]{minimal}
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\begin{document}$$g_{rr}$$\end{document} which often yields physically motivated solutions that describe the anisotropic matter distribution interior the astrophysical system. The physical availability of the obtained model, represents the physical characteristics of the solution is affirmed by performing several physical tests. It merits referencing that with the help of the observed mass values for six compact stars, we have predicted the exact radii for different values of χ\documentclass[12pt]{minimal}
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\begin{document}$$\chi $$\end{document}-coupling parameter. From this one can convince that the solution predicted the radii in good agreement with the observed values. Since the radius of MSP J0740+6620, the most massive neutron star observed yet is still unknown, we have predicted its radii for different values of χ\documentclass[12pt]{minimal}
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\begin{document}$$\chi $$\end{document}-coupling parameter. These predicted radii exhibit a monotonic diminishing nature as the parameter χ\documentclass[12pt]{minimal}
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\begin{document}$$\chi $$\end{document} going from -1\documentclass[12pt]{minimal}
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\begin{document}$$-1$$\end{document} to 1 gradually. The M–R curve generated from our solution can accommodate a variety of compact stars from the less massive (Her X-1) to super massive (MSP J0740+6620). So the present study uncovers that the modified f(R, T) gravity is an appropriate theory to clarify massive astrophysical systems, in any case, for χ=0.0\documentclass[12pt]{minimal}
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\begin{document}$$\chi =0.0$$\end{document} the standard consequences of the general relativity are recovered.
