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The present paper is devoted to investigating the possibility of getting stellar interiors for ultra-dense compact spherical systems portraying an anisotropic matter distribution employing the gravitational decoupling by means of Minimal Geometric Deformation (MGD) procedure within the modified theory of f(R,T) gravity. According to this theory, the covariant divergence of stress-energy tensor does not vanish, hence the movement of classical particles does not follow geodesics resulting in an extra acceleration which suffices the late-time acceleration of the universe without adopting to exotic matter fields. In this regard, we have considered the algebraic function as f(R, {\rm T})= R+2χT, the corresponding effective stress-energy tensor is conserved as well as the exact solutions are derived, where $χ$ indicates a coupling constant. Moreover, the physical quantities associated with the new solutions are well-behaved from the physical and mathematical point of view as well as free of geometrical singularities, violation of the causality condition, non-decreasing thermodynamic functions. Thereafter, the physical viability of the obtained model is affirmed by performing several physical tests of the main salient features such as energy density, radial, and tangential pressure, anisotropy effect, dynamical equilibrium, energy conditions, and dynamical stability. On the other hand, we have generated the M-R curves from our solutions in the four different scenarios, including GR, GR+MGD, f(R,T) and f(R,T)+MGD, and we found a perfect fit for many compact spherical objects in these scenarios by changing the gravitational decoupling constant αand the coupling constant χas free parameters. The present study reveals that the modified f(R,T) gravity through gravitational decoupling by means of MGD method is a suitable theory to explain compact stellar spherical systems....