Supersonic combustion is a major challenge in the development of hypersonic vehicles. To achieve efficient combustion within the combustor at crossflow Mach numbers ranging from 2 to 4, it is crucial to ensure rapid injection, mixing, and combustion processes. This is a major challenge for conventional injection schemes, such as transverse jets in supersonic crossflows, compared to their low-speed counterparts. In the farfield, the flow moves roughly at the same speed as the crossflow, and therefore the significant large-scale coherent structures that cause the fuel-air mixing through slow molecular diffusion also travel at high speeds. Near-field mixing thus becomes an important process as it becomes the major contributor to fuel and oxidizer mixing. The effect of different jet-to-crossflow momentum ratios is numerically investigated for a Mach 2.9 crossflow using an in-house adaptive mesh refinement-based compressible flow solver on a sonic ethylene jet injected into the supersonic crossflow. The non-reacting analysis focuses on the influence of momentum ratio on jet structure, penetration height, and mixing characteristics. Conclusive positive correlations between these parameters are identified, supported by comparisons with existing experimental studies. The reacting analysis focused on the ignition and flame stabilization for the different momentum ratio values and found that combustion is localized in the near-wall region on the windward side of the jet. The overall heat release was lower, and convection time scales dominated the slow reactive processes. The capabilities of AMR were leveraged to capture the jet and reaction zone structures with fidelity comparable to the DNS while maintaining a computational cost similar to LES.