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The quantum spin continuum and classical spin freezing, associated with a glassy state, represent two opposite extremes of a correlated electronic material. Here, we report the coexistence of a quantum spin continuum with a weak spin glass order in Co-doped CaRuO₃ perovskite near the chemical doping dependent metal-insulator transition boundary. Inelastic neutron measurements on Ca(Co_0.15Ru_0.85)O₃ at low temperature, T = 1.5 K, reveal a continuum spectrum in the Q-E space due to uncorrelated spin fluctuations. This persists across the glass transition at T_G~23 K. Furthermore, scaling of the dynamic susceptibility yields a very small scaling coefficient α~ 0.1, suggesting extreme locality of the dynamic properties. The experimental results indicate the realization of a narrow regime where the distinction between continuum dynamic behavior and glass-like regimes is reduced.