Power-domain non-orthogonal multiple access (NOMA) has emerged as a promising technology to enhance spectral efficiency in wireless networks by exploiting the power domain. However, existing NOMA schemes often rely on the assumption of significant channel gain differences among users, which may not hold in practical scenarios. To unlock the full potential of power-domain NOMA, a novel approach called reconfigurable intelligent surface (RIS)-based NOMA scheme is proposed. By adjusting the phase shifts at the RIS, desirable channel gain differences among users can be introduced, thereby optimizing system performance. Simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) enable the communication between the base station and users established on opposite planes of the STAR-RIS, while also allowing for the existence of direct links. In this study, we investigate the potential of RIS-aided NOMA systems, exploring their performance under generalized \(\alpha -\mu \) fading channel. Simulation results demonstrate that incorporating RIS in NOMA setups improves the overall system error performance. The impact of imperfect CSI on the system performance is also analyzed. Furthermore, the study shows that the STAR-RIS-NOMA system outperforms the RIS-NOMA system.