Abstract The β -Mn type Co x Zn y Mn 20− x − y compound, known for hosting magnetic skyrmions beyond room temperature, plays a key role in understanding complex magnetic behaviors and advancing spintronics, particularly in skyrmion-based magnetic data storage and processing. In this study, we thoroughly investigated the field-dependent critical behavior of the cubic β -Mn type Co 8.68 Zn 8.65 Mn 2.67 single-crystal, focusing on magnetic isotherms near its Curie temperature. Employing methods such as modified Arrott plots, the Kouvel–Fisher method, and critical isothermal analysis, we determined the critical exponents β, γ , and δ , which are 0.456 ± 0.001, 1.144 ± 0.016, and 3.510 ± 0.040 respectively. According to renormalization group theory, the magnetic interaction in this system decays with distance r as J(r)≈r−4.7 . These values indicate that the Co 8.68 Zn 8.65 Mn 2.67 system’s critical behavior is intermediate between the mean-field model and the 3D Heisenberg model. Specifically, this decay pattern indicates that as temperature increases, the critical behavior of Co 8.68 Zn 8.65 Mn 2.67 may approach the mean-field model, while at low temperatures, spin fluctuations and stronger local interactions may cause its behavior to resemble that of the Heisenberg model.