Spin‐state transition, also known as spin crossover, plays a key role in diverse systems, including minerals and biological materials. In theory, the boundary range between the low‐ and high‐spin states is expected to enrich the transition and give rise to unusual physical states. However, no compound that realizes a nearly degenerate critical range as the ground state without requiring special external conditions has yet been experimentally identified. This study reports that, by comprehensive measurements of macroscopic physical properties, X‐ray diffractometry, and neutron spectroscopy, the Sc substitution in LaCoO3 destabilizes its nonmagnetic low‐spin state and generates an anomalous paramagnetic state accompanied by the enhancement of transport gap and magneto‐lattice‐expansion as well as the contraction of Co─O distance with the increase of electron site transfer. These phenomena are not well described by the mixture of conventional low‐ and high‐spin states, but by their quantum superposition occurring on the verge of a spin‐state transition. The present study enables us to significantly accelerate the design of new advanced materials without requiring special equipment, based on the concept of quantum spin‐state criticality.