In this work, the hydration mechanism, influencing factors, and mineral interactions of binders composed of ordinary Portland cement (OPC), calcium sulphoaluminate cement (CSA), and anhydrite (C \({\overline{\text{S}}}\) ) were studied. Results show that the ternary system's fast setting, rapid hardening, and dimensional stability could be adjusted by the OPC content and the ratio of anhydrite/tetracalcium sulfoaluminate (C4A3 \({\overline{\text{S}}}\) ), which determine the generation of ettringite (AFt). In the early stage of hydration, an increase in the rate of ettringite generation promotes the fast setting and rapid hardening rate of the ternary system. In the middle and later stages of hydration, an increase in the number of ettringite affects strength development and dimensional stability. When the molar ratio of anhydrite/tetracalcium sulfoaluminate is below 4.4, ettringite and aluminum gel (AH3) are the primary products, shifting to predominantly ettringite when the ratio exceeds 5.8. The optimal composition with 58.1% OPC, 33.4% CSA, and 8.5% C \({\overline{\text{S}}}\) , displayed an initial setting time of 10 min, final setting time of 14 min, 2-h compressive strength of 25.6 MPa, 28-day compressive strength of 76.1 MPa, and 28-day dry shrinkage of only − 0.0065%. The findings provided a theoretical and scientific foundation for the design and preparation ternary fast setting and rapid hardening binders.