  The purpose of this paper is to study charged compact stars using extended
gravitational theory, also known as $f(\mathcal{R}, \mathcal{G}, \mathcal{T})$
gravity. Alternatively, this theory is also called $f(\mathcal{R}, \mathcal{T},
\mathcal{G})$ gravity. The symbols $\mathcal{R}, \mathcal{G}$, and
$\mathcal{T}$ denote the Ricci Scalar, the Gauss-Bonnet invariant, and the
trace of the energy-momentum tensor, respectively. We suggested several
plausible models in the framework of this new gravity theory, and then used
these models to explore several physical properties of compact objects of
relativistic nature. This research also takes into account three famous compact
stars: Vela X-1 (CS1); SAXJ1808.4-3658 (CS2); and 4U1820-30 (CS3). Moreover,
using the suggested models, the physical nature of anisotropic stress, energy
density, various energy conditions (ECs), the state of equilibrium, interior
stability, mass variations, compactness, anisotropy, electric charge, and
electric field intensity are analysed for considered compact stars. Different
plots of the above-mentioned quantities are presented for this analysis.
Conclusively, the ECs are satisfied, and the compact stars have a significant
dense core.
