<p>In this study, we first propose the functional quadratic spatial autoregressive model, which can effectively capture spatial dependencies, linear relationships and nonlinear interactions in functional data. Then, we develop a generalized statistical inference framework for this model, where the functional component is treated by principal component analysis, followed by parameter estimation employing the generalized method of moments. Subsequently, we construct two residual-based test statistics to assess the model’s goodness of fit. Under some regularity conditions, we derive the asymptotic properties, encompassing the asymptotic normality of estimators for the finite parametric vector, the optimal convergence rate for nonparametric functions, and the asymptotic distributions of the proposed test statistics under null hypothesis and local or global alternative hypothesis. To determine the critical values for model checking statistics, we introduce a wild bootstrap procedure, and the asymptotic validity of this bootstrap-based testing approach is also discussed. The finite-sample performance of our methodology is evaluated through Monte Carlo simulations, and its practical usefulness is illustrated through two real-data applications to Spanish meteorological data and economic growth data. The results substantiate the efficacy of our approach in the real-world scenarios.</p>