  The present study provides an in-depth analysis of the anisotropic matter
distribution and various physical aspects of compact stars in the context of a
$f(R,G)$-gravity framework. In order to gain an exhaustive understanding of
these aspects, our study focuses on three particular compact stars: VELA X-1
(CS1), SAXJ1808.4-3658 (CS2), and 4U1820-30 (CS3). We conducted calculations on
the relevant characteristics of these compact stars by employing three
different models of $f(R,G)$-gravity. As a convenient approach, the
$f(R,G)$-gravity is organized into two distinct components, which include
$f_1(R)$ and $f_2(G)$. The $R$ dependent component is modeled similarly to the
Hu-Sawicki approach, while for modeling the $G$ dependent component, we chose
logarithmic and power law-like approaches and suggested three viable gravity
models. Graphical methods are used to analyze the physical properties of the
compact stars in the domain of suggested models of gravity.
