The complexity of microscopic nuclear many-body wave functions hindered a deeper understanding of nucleon clustering driven by complex nucleon-nucleon correlations. To address this, a universal four-fermion formation framework (U4F) is developed within the configuration-interaction shell model. The U4F enables microscopic analysis of the a component in mixed quartet configurations and reveals the correlation between a formation and the underlying nucleon-nucleon interaction, with consideration of full many-body correlations within a model space. The a formation in the a-decaying yrast band and high-spin isomer of 212Po is investigated using the U4F. Theoretical results agree with the a formation amplitude extracted from the measured a decay half-life and decay energy. The analysis shows that the reduction of a formation with increasing spin in the yrast band arises from the competition between the growing purity of quartet configurations and the diminishing realistic a component within them. Finally, the a-decaying 18+ isomer of 212Po is suggested as an a-reducing phase generated by the mixing of the 18+1 and 18+2 states.