The study of spatial econometrics has developed rapidly and has found wide applications in many different scientific fields, such as demography, epidemiology, regional economics, and psychology. With the deepening of research, some scholars find that there are some model specifications in spatial econometrics, such as spatial autoregressive (SAR) model and matrix exponential spatial specification (MESS), which cannot be nested within each other. Compared with the common SAR models, the MESS models have computational advantages because it eliminates the need for logarithmic determinant calculation in maximum likelihood estimation and Bayesian estimation. Meanwhile, MESS models have theoretical advantages. However, the theoretical research and application of MESS models have not been promoted vigorously. Therefore, the study of MESS model theory has practical significance. This paper studies the quasi maximum likelihood estimation for matrix exponential spatial specification (MESS) varying coefficient panel data models with fixed effects. It is shown that the estimators of model parameters and function coefficients satisfy the consistency and asymptotic normality to make a further supplement for the theoretical study of MESS model.