Based on the extended Huygens–Fresnel principle and mode expansion theory, we derive the expression for the Coherence-Orbital Angular Momentum (COAM) matrix of twisted Gaussian Schell-model (TGSM) beams propagating through non-Kolmogorov turbulence. Using numerical simulations, we compare the evolution characteristics of the COAM matrix in free space and under non-Kolmogorov turbulence conditions. The study analyzes the variation patterns in the absolute values, real parts, and imaginary parts of the COAM matrix elements under different topological charges, and provides a detailed investigation of the influence of various beam parameters and turbulence parameters on these elements. The results show that by selecting appropriate parameters, the negative impact of turbulence on the correlation between orbital angular momentum (OAM) modes can be effectively mitigated. This work provides theoretical support for parameter selection and optimization in atmospheric optical communication systems.