  This paper analyzes the anisotropic stellar evolution governed by a
polytropic equation of state in the framework of $f(R,T,Q)$ gravity, where
$Q=R_{ab}T^{ab}$. We construct the field equations, hydrostatic equilibrium
equation and trace equation to obtain their solutions numerically under the
influence of $\sigma R^{2}+\gamma Q$ gravity model, where $\sigma$ and $\gamma$
are arbitrary constants. We examine the dependence of various physical
characteristics such as radial/tangential pressure, energy density, anisotropic
factor, total mass and surface redshift for specific values of the model
parameters. The physical acceptability of the considered model is discussed by
verifying the validity of energy conditions, causality condition, and adiabatic
index. We also study the effects arising due to the strong non-minimal
matter-curvature coupling on anisotropic polytropes. It is found that the
polytropic stars are stable and their maximum mass point lies within the
required observational Chandrasekhar limit.
