Ammonia, being a carbon-free fuel, is garnering increasing attention in the combustion community. However, its application is still impeded by its limited stability range and significantly NOx emissions. This study delves into the impact of primary and overall equivalence ratios (ϕpri and ϕovr) on emissions production in ammonia–hydrogen co-firing flames, utilizing a two-stage swirling model gas turbine combustor. The emissions concentration is measured using Fourier Transform Infrared Spectroscopy (FTIR). The physical and chemical processes influencing emissions production are comprehensively analyzed through a combination of Large Eddy Simulation (LES) and Flamelet-Generated Manifold (FGM) method. The reliability of the simulation is validated by the experimental data, showing a good capability in predicting the combustion. Results indicate that the two-stage combustion strategy exhibits significantly controlling effects on NOx and unburned NH3 emission. The NO emission exhibits a non-monotonic variation with ϕpri, reaching its lowest value at ϕpri≈ 1.2. Further analysis shows that ϕpri plays a crucial role in determining the temperature and OH concentration in the primary combustion zone, thereby influencing NOx production in this area. When the primary zone is operated at lean condition, the reduction on NO in secondary zone is primarily attributed to dilution effect by the secondary air. In contrast, when ϕpri> 1, the concentrations of the main emissions in secondary zone are dominated by chemical effects. In this scenario, unburned NH3 and H2 from the primary zone are consumed, resulting in a substantial production of NO in the secondary combustion zone. Additionally, with an increase in ϕpri, the secondary NO production also increases. The ϕovr exhibits two considerable effects. On one hand, an increase in ϕovr results in a higher local equivalence ratio in the secondary zone, thereby promoting local NOx production. Simultaneously, the elevated flame temperature enhances the consumption of N2O. On the other hand, the rise in ϕovr results in a reduction in vortex scale and residence time in the secondary combustion zone, leading to a decrease in local NO production.