Magnetic materials of strongly correlated origin are at the forefront of research in the exploration of new quantum mechanical properties involving spin and charges. Quantum magnetic material with certain intrinsic functionalities, such as continuously fluctuating spins to the lowest accessible temperature - reminiscing a liquid pattern, is argued to form a new phase of matter. Envisaging a phenomenon where the continuously fluctuating spins are also randomly frozen in space, can diminish the distinction between the two opposite extremes of quantum and classical magnetism. Here, we report new evidence in this regard where the coexistence of quantum spin continuum with a spin glass order in Co-doped CaRuO₃ perovskite is demonstrated. In experimental investigations of Co-doped CaRuO₃ perovskite, we find that (a) a continuum spectrum in the energy-momentum space, due to the uncorrelated spin fluctuations, persists across the weak spin glass transition at T_G ≅ 23 K and (b) the quantum fluctuation of magnetic moment is spatially confined to individual sites only, thereby making it an extremely local event. Thus, the fluctuating spins, at a given time, are also randomly frozen macroscopically. The experimental observations suggest the discovery of a new magnetic phase at the cross-road of classical and quantum physics in strongly correlated perovskite materials.