In many applications of regression analysis, regression coefficients usually satisfy constraint conditions and error terms are heteroscedastic. This paper considers statistical inference of partially linear spatial autoregressive model with constraint conditions and heteroscedasticity. The constrained estimators of unknown parameters and function are established by combining local polynomial smoothing method, generalized method of moments and Lagrange multiplier method, and their asymptotic properties are investigated under appropriate regularity conditions. Furthermore, a Wald test statistic is constructed to test appropriateness of a linear constraint condition on the regression coefficients. It is shown that the proposed test statistic asymptotically follows Chi-squared distribution under both null and alternative hypotheses. Simulation studies and real data analysis are conducted to demonstrate finite sample property of the proposed estimation and testing methods.