  The main goal of this work is to provide a comprehensive study of
relativistic structures in the context of recently proposed {$\mathcal{R}+
\alpha \mathcal{A}$} gravity, where $\mathcal{R}$ is the Ricci scalar, and
$\mathcal{A}$ is the anti-curvature scalar. For this purpose, we examine a new
classification of embedded class-I solutions of compact stars. To accomplish
this goal, we consider an anisotropic matter distribution for {$\mathcal{R}+
\alpha \mathcal{A}$ gravity model} with static spherically symmetric spacetime
distribution. Due to highly non-linear nature of field equations, we use the
Karmarkar condition to link the $g_{rr}$ and $g_{tt}$ components of the metric.
Further, we compute the values of constant parameters using the observational
data of different compact stars. It is worthy to mention here that we chose a
set of twelve important compact stars from the recent literature namely
$4U~1538-52$, $SAX~J1808.4-3658$, $Her~X-1$, $LMC~X-4$, $SMC~X-4$,
$4U~1820-30$, $Cen~X-3$, $4U~1608-52$, $PSR~J1903+327$, $PSR~J1614-2230$,
$Vela~X-1$, $EXO~1785-248$. To evaluate the feasibility of {$\mathcal{R}+
\alpha \mathcal{A}$ gravity model}, we conduct several physical checks, such as
evolution of energy density and pressure components, stability and equilibrium
conditions, energy bounds, behavior of mass function and adiabatic index. It is
concluded that {$\mathcal{R}+ \alpha \mathcal{A}$} gravity supports the
existence of compact objects which follow observable patterns.
