We study the 3D hyperdissipative Navier-Stokes equations on the torus. It is well-known that, due to Lions, for any L^2 divergence-free initial data, there exist unique smooth Leray-Hopf solutions when the viscosity exponent is larger than 5/4. We prove that even in this high dissipative regime, the uniqueness would fail in the supercritical spaces in view of the generalized Ladyzenskaja-Prodi-Serrin condition. This talk is based on the joint work with Prof. Yachun Li, Prof. Deng Zhang and Dr. Zirong Zeng.