Theoretical and experimental results are presented that introduce topology into the field of plasmonic and optical resonances in ring resonators. Due to the occurrence of the Berry phase in non-trivial evolution, plasmon/photon modes with non-integer numbers of wavelengths along the circumference are revealed in metallic/dielectric Möbius rings that do not exist in conventional ring resonators. Notably, a variable Berry phase ranging from 0 to π was generated and observed in optical Möbius-strip microcavities. This contrasts with previous reports in optical, electronic, and magnetic Möbius topology systems, which suggest only a fixed Berry phase of π. In cone-shaped anisotropic microtube resonators, optical spin–orbit coupling is enabled for the generation of the Berry phase acquired in a non-cyclic and non-Abelian evolution. These topology-induced effects hold promising potential for applications in manipulating photons in on-chip integrable quantum devices.