  The objective of our current study is to explore novel aspects of a
stationary anisotropic relativistic hybrid compact star that consists of quark
matter (QM) in its core and ordinary baryonic matter (OBM) in its crust. This
study has been done by adopting separate equations of states (EoSs) for quark
matter and baryonic matter. The MIT bag model equation of state
$p_{q}=\frac{1}{3}(\rho_{q}-4B)$ has been used to demonstrate a correlation
between the density and pressure of weird quark matter in the interior of the
star. In addition, we present a simple linear equation of state
$p_{r}=\beta_{1}\rho-\beta$ that links radial pressure and matter density for
OBM. The stellar model was formulated within the context of
$f(\mathcal{R},\mathcal{A})$ gravity, utilizing a linear correlation between
Ricci tensor $\mathcal{R}$ and anticurvature scaler $\mathcal{A}$.To solve the
field equations of this novel alternative gravity, we employ the Krori and
Barua approach to the metric potentials. The validity of our suggested model is
assessed using the graphical approach, while ensuring that the conditions are
physically feasible. Our focus is specifically on the tiny celestial object
known as LMC X-4 [$\text{M} =
(1.04^{+0.09}_{-0.09})M_{\odot};\text{R}=8.301^{+0.2}_{-0.2}\text{km}$], which
we consider a viable candidate for a strange quark star. We want to clarify the
model's physical validity by examining a variety of physical assessments,
including dynamical equilibrium, energy conditions, compactness factor, mass
function, and surface redshift. The resulting outcome confirms the authenticity
of the hybrid star model under analysis.
