An ammonia-hydrogen-fuelled combustion engine is seen as potentially carbon-free technology for the future transport and energy sectors. On the one hand, the use of ammonia poses challenges for engine applications due to its resistance to combustion under typical operating conditions. This problem can be eliminated by co-combustion of ammonia with hydrogen, which acts as an ignition enhancer. On the other hand, burning ammonia produces harmful emissions, including NOx and N2O, and its incomplete combustion results in ammonia slip. To address these challenges, we numerically investigate combustion and emissions formation in a spark-ignition gasoline engine fuelled with ammonia-hydrogen blends. The focus is on combustion stability, expressed by cycle-to-cycle variation, flame propagation and flame regimes, and the formation of nitrogen emissions such as NO, NO2, and N2O. Simulations are conducted using a stochastic reactor model of engine in-cylinder processes. A detailed reaction kinetics mechanism is employed to describe the combustion of ammonia-hydrogen fuel and the formation of exhaust emissions. Simulations are based on experimental data from a gasoline engine operated at different air-to-fuel and ammonia-to-hydrogen ratios. The results provide further insights into the combustion of ammonia-hydrogen fuel under spark-ignition engine-relevant operating conditions.