  The present work is to introduce a new kind of modified gravitational theory,
named as $f(\mathcal{R,G,T})$ (also $f(\mathcal{R,T,G})$) gravity, where
$\mathcal{R}$ is the Ricci scalar, $\mathcal{G}$ is Gauss-Bonnet invariant and
$\mathcal{T}$ is the trace of the energy-momentum tensor. With the help of
different models in this gravity, we investigate some physical features of
different relativistic compact stars. For this purpose, we develop the
effectively modified field equations, conservation equation, and the equation
of motion for test particle. Then, we check the impact of additional force
(massive test particle followed by a non-geodesic line of geometry) on compact
objects. Furthermore, we took three notable stars named as $Her X-1$,
$SAXJ1808.4-3658$ and $4U1820-30$. The physical behavior of the energy density,
anisotropic pressures, different energy conditions, stability, anisotropy, and
the equilibrium scenario of these strange compact stars are analyzed through
various plots. Finally, we conclude that the energy conditions hold, and the
core of these stars is so dense.
