Automatic modulation classification (AMC) is a fundamental task in modern wireless communication systems, crucial for enabling adaptive spectrum management and intelligent signal processing. This paper investigates the performance enhancement of AMC through the integration of ResNet and advanced test-time adaptation (TTA) techniques. We first demonstrate the superiority of ResNet over conventional CNNs on two benchmark datasets, RML2016.10A and RML2018.01A, especially under low SNR conditions. To further improve robustness against distribution shifts in practical deployments, we propose two novel TTA methods: Test-Time Adaptation with Temperature Scaling (TATS) and Test-Time Adaptation with Self-Distillation (TASD). These methods adaptively refine the model predictions during inference by optimizing batch normalization parameters, without requiring labeled target data or structural changes to the pretrained model. Experimental results show that TATS and TASD consistently outperform mainstream TTA approaches, achieving significant accuracy gains across varying SNR levels. Our work highlights the potential of combining deep residual learning with adaptive inference strategies to build more resilient AMC systems suitable for real-world wireless environments.