In underwater robots, accurate identification of small fish is still a major challenge, because small fish move faster and occupy less screen space, which requires higher detection flexibility and receptive field of the model. To solve this challenge, we propose a high-precision small fish identification and tracking method named YOLO8-FASG in this paper. Specifically, the proposed method is improved in three aspects based on the YOLOv8 framework. First, Alterable Kernel Convolution(AKConv) is used in the neck network of the model to automatically adjust the shape of the convolution kernel according to the size and shape of the object. In this way, the shape and contour characteristics of rapidly changing fish can be captured more accurately and efficiently; Second, we introduce a global attention mechanism (GAM) to broaden the receptive field of the model by enhancing attention to fish features from the two dimensions of channel and space; Third, we employ Simplified Spatial Pyramid Pooling-Fast(SimSPPF) to replace the standard Spatial Pyramid Pooling-Fast(SPPF) to enhance prediction accuracy. These improvements enable the model to effectively extract image features of small, fast fish, thereby improving the robot's accuracy in identifying small fish underwater. Experiments results in the public dataset Fish4Knowledge show that YOLO8-FASG performs significantly better than traditional YOLOv8 in underwater environments. Specifically, Precision and Recall increased by 1.6% and 3.5% respectively, while mAP50 and mAP50-95 increased by 1.3% and 6.1% respectively, and our method provides an effective solution for underwater robots to identify fish schools.