In the context of the industrial Internet of Things (IIoT), communication devices are typically mobile, increasing the complexity and diversity of channels due to metal device occlusion. A crucial aspect of this intricate environment is the development of an authentication scheme based on physical layer channel characteristics. One approach to achieving this is through deep learning, which is a hot topic in physical layer authentication. However, designing a network that is suitable for channel classification tasks and establishing a reasonable training procedure that leads to high authentication accuracy can be challenging. To address the physical layer authentication of mobile devices in IIoT, we implement ResNet to extract channel features of Channel State Information (CSI) from different transmitters and classify them at the network output layer, enabling authentication decisions based on classification results. To improve accuracy and speed up network convergence, we utilize the exponentially averaging data augmentation algorithm and parameter-based transfer learning strategy during the training procedure. Simulation results demonstrate that multi-user physical layer authentication based on ResNet can achieve higher authentication accuracy as the number of network layers increases. The data augmentation and transfer learning are proved to improve the authentication accuracy. Numerical results on NIST industrial datasets reveal that the authentication scheme based on ResNet50 can achieve 99.64% authentication accuracy in scenarios with four users present, which is 32.68% higher than existing algorithm.