Mirror-symmetric microring resonators perturbed by periodically spaced scatterers induce symmetric optical vortex superimposition states. In this letter, we theoretically and numerically show that a broken mirror symmetric resonator can induce asymmetric optical orbital angular momentum (OAM) superimposition states. The asymmetric OAM behaviour is due to the chiral and non-orthogonal resonator modes at exceptional point. Potential applications of the OAM beam emission behavior could include information processing and particle micromanipulation with functionality-switching capabilities.