  This paper investigates some particular anisotropic star models in
$f(\mathcal{R},\mathcal{T},\mathcal{Q})$ gravity, where
$\mathcal{Q}=\mathcal{R}_{\omega\alpha}\mathcal{T}^{\omega\alpha}$. We adopt a
standard model
$f(\mathcal{R},\mathcal{T},\mathcal{Q})=\mathcal{R}+\varpi\mathcal{Q}$, where
$\varpi$ indicates a coupling constant. We take spherically symmetric spacetime
and develop solutions to the modified field equations corresponding to
different choices of the matter Lagrangian by applying `embedding class-one'
scheme. For this purpose, we utilize $\mathbb{MIT}$ bag model equation of state
and investigate some physical aspects of compact models such as RXJ 1856-37,~4U
1820-30,~Cen X-3,~SAX J 1808.4-3658 and Her X-I. We use masses and radii of
these stars and employ the vanishing radial pressure condition at the boundary
to calculate the value of their respective bag constant $\mathfrak{B_c}$.
Further, we fix $\varpi=\pm4$ to analyze the behavior of resulting state
variables, anisotropy, mass, compactness, surface redshift as well as energy
bounds through graphical interpretation for each star model. Two different
physical tests are performed to check the stability of the developed solutions.
We conclude that $\varpi=-4$ is more suitable choice for the considered
modified model to obtain stable structures of the compact bodies.

General Relativity and Quantum Cosmology