  The manifesto of the current article is to investigate the compact
anisotropic matter profiles in the context of one of the modified gravitational
theories, known as $f(\mathcal{R}, \mathcal{T})$ gravity, where $\mathcal{R}$
is a Ricci Scalar and $\mathcal{T}$ is the trace of the energy-momentum tensor.
To achieve the desired goal, we capitalized on the spherical symmetric
space-time and utilized the embedding class-1 solution via Karmarkar's
condition in modeling the matter profiles. To calculate the unidentified
constraints, Schwarzschild exterior solution along with experimental statistics
of three different stars LMC X-4, Cen X-3, and EXO 1785-248 are taken under
consideration. For the evaluation of the dynamical equations, a unique model
$f(\mathcal{R}, \mathcal{T})=\mathcal{R}+\beta \mathcal{R}^2+\lambda
\mathcal{T}$ has been considered, with $\beta$ and $\lambda$ being the real
constants. Different physical aspects have been exploited with the help of
modified dynamical equations. Conclusively, all the stars under observations
are realistic, stable, and are free from all singularities.
