This paper presents a novel rate-splitting multiple access (RSMA) framework with partial reconfigurable intelligent surface (PRIS) selection over Nakagami-m fading channels, a scenario that has not been comprehensively analyzed in prior works. To this end, we conduct a detailed performance analysis of a wireless communication system that incorporates multiple reconfigurable intelligent surfaces (RISs) as cooperative relays. The proposed framework integrates RSMA with a PRIS selection strategy, enabling efficient data transmission from the base station (BS) to two users with distinct channel conditions. Closed-form expressions for the outage probability and achievable throughput are derived over independent and non-identically distributed (i.n.i.d.) Nakagami-m fading channels. The analysis highlights the role of PRIS in enhancing system efficiency and ensuring fair resource allocation between users. In addition, asymptotic evaluations offer deeper insights into the system’s behavior under varying channel dynamics. Simulation results are provided to validate the theoretical findings, demonstrating a close match with the analytical expressions and confirming the robustness of the proposed approach.