This letter investigates an unconventional RIS- aided non-orthogonal multiple access (NOMA) system to achieve spectral-efficient full-duplex (FD) ultra-reliable low-latency communication (URLLC) systems. In particular, we focus on sum-rate maximization under finite-block length coding for the considered system by jointly optimizing power allocation at each user and beamforming at the RIS, while ensuring that the minimum rate, delay, and reliability requirements are satisfied. To solve the formulated joint optimization problem, we proposed an alternate optimization framework that solves the sub-problems of power allocation and beamforming alternatively based on general convex approximations. Numerical results validate that the proposed FD scheme achieves 90% and 40% better rate performance than its counterpart orthogonal and half-duplex schemes, respectively. Moreover, the exploitation of RIS-aided network for the considered system provides rate performance amelioration up to 40-50% and 56-80% compared to the random phase-shifting at the RIS and the system without RIS, respectively.