Nonclassical phenomena can be enhanced by introducing q-deformation in optomechanical systems. This motivates investigation of the optical response in a q-deformed linearly coupled optomechanical system. The system consists of two deformed cavities that are linearly coupled to the motion of mechanical mirrors, and the cavities are coupled to each other by transmission strength parameter. This study shows that compared to non-deformed cases, the deformed system exhibits more rapid phase transition at the positions of transparency windows, causing stronger and enhanced fast and slow light phenomena. Moreover, in the region 0 < q < 0.5, the optomechanical system results in gain. Additionally, for a fixed deformation of cavities, by tuning the tunneling strength and optomechanical coupling, one can observe a delay and advancement in probe field in the order of milliseconds and even above milliseconds for fine-tuning of the coupling parameters. Finally, the bridge between mathematical and physical models is built by assuming the deformation to be a primitive root of unity, which indicates a class of anyon models. These results demonstrate that q-deformation provides a novel method for manipulating and significantly enhancing optical phenomena not only in arbitrarily deformed optomechanical systems but also in anyon models.