While the Internet of Things (IoT) technology is booming and offers huge opportunities for information exchange, it also faces unprecedented security challenges. As an important complement to the physical layer security technologies for IoT, radio frequency fingerprinting (RFF) is of great interest due to its difficulty in counterfeiting. Recently, many machine learning (ML)-based RFF algorithms have emerged. In particular, deep learning (DL) has shown great benefits in automatically extracting complex and subtle features from raw data with high classification accuracy. However, DL algorithms face the computational cost problem as the difficulty of the RFF task and the size of the DNN have increased dramatically. To address the above challenge, this paper proposes a novel costeffective early-exit neural network consisting of a complex-valued neural network (CVNN) backbone with multiple random forest branches, called hybrid CVNN-RF. Unlike conventional studies that use a single fixed DL model to process all RF samples, our hybrid CVNN-RF considers differences in the recognition difficulty of RF samples and introduces an early-exit mechanism to dynamically process the samples. When processing "easy" samples that can be well classified with high confidence, the hybrid CVNN-RF can end early at the random forest branch to reduce computational cost. Conversely, subsequent network layers will be activated to ensure accuracy. To further improve the early-exit rate, an automated multi-dimensional early-exit strategy is proposed to achieve scheduling control from multiple dimensions within the network depth and classification category. Finally, our experiments on the public ADS-B dataset show that the proposed algorithm can reduce the computational cost by 83% while improving the accuracy by 1.6% under a classification task with 100 categories.