Reconfigurable intelligent surface (RIS), nonorthogonal multiple access (NOMA), and underwater optical wireless communication (UOWC) are paradigms of technologies that drive the development of next generation communication systems. In this paper, we investigate the performance of a NOMA-based RIS-assisted hybrid radio frequency (RF)-UOWC system. The ship works as a relay that redirects the received signal to two underwater destinations simultaneously. Due to the interruption of the direct link between the base station and the ship floating on the surface of the water, communication will be carried out via an RIS fixed to an intermediate building. In this paper, we provide new analytical expressions for the outage probability (OP), asymptotic analyses of the OP, and diversity order (D) to gain insights into the system performance. The results showed that the diversity order depends on the UOWC receiver detection technique. In the end, we illustrated that the NOMA-based RIS-assisted system significantly improves the outage performance of hybrid RF-UWOC systems over a benchmark system.