In this paper, we study the construction of black string thin-shell wormhole models with generalized Chaplygin gas under the effect of minimally coupled modified gravity with quadratic correction in the Ricci scalar using the “cut and paste” method. We use junction conditions in geometrical representation for matching between two space-times across the hypersurface \(\Sigma \), recently computed by Rosa (Phys Rev D 103:104069, 2021). In this scenario, we assumed the matter sector is demonstrated by isotropic perfect fluid distribution. We determine the distinct components of Lanczos equations in the context of a considered quadratic model by employing generalized Chaplygin gas. We investigate static stable solutions utilizing radial perturbation in the perspective of the considered gravity. The positive value of the second-order derivative of potential around the throat radius might be interpreted as the stability criterion. For the widest feasible range of model parameters, the impact of mass and equation of state parameter is also investigated via the constructed equations. We also examine the stable and unstable static black string thin-shell wormhole solutions and illustrate them graphically.

在本文中，我们研究了使用“剪切和粘贴”方法在 Ricci 标量中进行二次修正的最小耦合修正重力作用下构建广义 Chaplygin 气体的黑弦薄壳虫洞模型。我们使用几何表示中的结点条件来匹配超曲面\(\Sigma \)上的两个时空，最近由 Rosa (Phys Rev D 103:104069, 2021) 计算。在这种情况下，我们假设物质部分由各向同性的完美流体分布来证明。我们通过使用广义 Chaplygin 气体，在考虑的二次模型的背景下确定 Lanczos 方程的不同分量。我们从考虑重力的角度研究利用径向扰动的静态稳定解。喉部半径周围势能的二阶导数的正值可以解释为稳定性准则。对于最广泛的模型参数可行范围，还通过构造的方程研究了质量和状态方程参数的影响。我们还研究了稳定和不稳定的静态黑弦薄壳虫洞解，并以图形方式说明它们。