In this paper, we studied the possible existence of anisotropic spherically symmetric solutions in the arena of modified \(f(\textit{G}, \textit{T})\)-gravity theory. To supply exact solutions of the field equations, we consider that the gravitational Lagrangian can be expressed as the generic function of the quadratic Gauss–Bonnet invariant \(\textit{G}\) and the trace of the stress–energy tensor \(\textit{T}\), i.e., \(f(\textit{G},\textit{T}) = \textit{G}^2 + \chi \textit{T}\), where \(\chi \) is a coupling parameter. We ansatz the gravitational potential: \(g_{rr} \equiv e^{\lambda (r)}\) from the relationship quasi-local mass function, \(e^{-\lambda }=1-\frac{2m(r)}{r}\), and we obtained the gravitational potential: \(g_{tt} \equiv e^{\nu (r)}\) via the embedding class one procedure. In this regard, we investigated that the new solution is well analyzed and well comported through various physical and mathematical tests, which confirmed the physical viability and the stability of the system. The present investigation uncovers that the \(f(\textit{G},\textit{T})\)-gravity via embedding class one approach is a well acceptable to describe compact systems, and we successfully compared the effects of all the necessary physical requirements with the standard results of \(f(\textit{G})\)-gravity, which can be retrieved at \(\chi = 0\).

在本文中，我们研究了修正的\（f（\ textit {G}，\ textit {T}）\）-重力理论领域中各向异性球对称解的可能存在。为了提供场方程的精确解，我们认为引力拉格朗日可以表示为二次高斯-邦内不变式\（\ textit {G} \）和应力-能量张量\（\ textit {T} \），即\（f（\ textit {G}，\ textit {T}）= \ textit {G} ^ 2 + \ chi \ textit {T} \），其中\（\ chi \ ）是一个耦合参数。我们从准局部质量函数关系中解析出引力：\（g_ {rr} \ equiv e ^ {\ lambda（r）} \），\（e ^ {-\ lambda} = 1- \ frac {2m（r）} {r} \），我们获得了引力：\（g_ {tt} \ equiv e ^ {\ nu（r）} \）通过嵌入类一过程。在这方面，我们调查了通过各种物理和数学测试对新解决方案进行了很好的分析和比较合理的结果，从而确认了系统的物理可行性和稳定性。本研究发现，通过嵌入类一方法的\（f（\ textit {G}，\ textit {T}）\）-重力对于描述紧凑型系统是可以接受的，并且我们成功地比较了所有必要条件的效果物理要求，其标准结果为\（f（\ textit {G}）\）- gravity，可以在\（\ chi = 0 \）处进行检索。