Abstract. In MISO systems, novel communication technologies such as NOMA and multicast transmission have attracted widespread attention to meet the diverse needs of users. However, traditional NOMA and multicast transmission schemes have certain limitations in dynamic interference management and resource allocation. To resolve this issue, this paper proposes a RSMA scheme assisted by phase quantized Intelligent Reflecting Surface (IRS) for downlink MISO systems with nonorthogonal transmission of unicast and multicast signals. In this scheme, through reconfiguring unicast and multicast signals and combining them into a super-common stream and partial unicast messages, RSMA achieves dynamic interference management of multi-user while effectively separating unicast and multicast streams. To maximize the weighted sum rate(WSR), we put forward an alternating optimization(AO) algorithm that utilizes Weighted Minimum Mean Square Error (WMMSE) estimation and convex set intersection representation, which jointly optimizes the equivalent beamforming matrix,rate allocation and phase shift matrix. Simulation results illustrate that the proposed single-layer RSMA exhibits performance closer to that of DPC encoding compared to traditional NOMA and MULP schemes. Furthermore, we extensively investigate the relationship between the WSR of RSMA and system parameters, providing important guidance for practical engineering applications.