Power system reliability hinges on accurate and timely fault classification, yet many real-world scenarios face data scarcity due to logistical and economic constraints. Traditional methods often struggle to maintain performance with limited training samples, creating a critical gap in practical applications. Fault classification in power systems often requires robust models that can be generalized from limited data. Traditional deep learning approaches, while highly effective, usually need large datasets to achieve acceptable performance. In this paper, we propose a novel convolutional neural networks (CNN) framework for fault classification tasks using small-scale databases. This is novel because it leverages transfer learning to adapt a pre-trained model in deep learning to the target domain of fault classification. Compared with other methods, our approach minimizes the dependency on large datasets besides achieving high accuracy and generalizability. Extensive experiments demonstrate that the proposed approach achieves state-of-the-art performance, validating its efficacy for scenarios with limited data availability. This research provides an essential step in applying deep learning to the fault classification problem of limited data resources, further pushing toward practical and accessible solutions for the field.