Around the globe, several fish species are on the verge of extinction due to overfishing and environmental degradation. An efficient automated fish monitoring system is crucial for rapid and accurate identification of fish species in water bodies. Deep Learning (DL)-based fish species recognition methodologies are highly suitable, as they offer efficient image classification with improved accuracy compared to traditional methods. However, these models are prone to overfitting, and there are chances for the performance of classifiers to be skewed toward common fish species due to the limited availability of samples. To address these issues, in this paper, a Slim Pre-Trained Network with Extreme Kernel Machine (SPTN-EKM)-based fish recognition mechanism is proposed. It focuses on integrating the benefits of SPTN with EKM such that precise classification is achieved. The proposed SPTN-EKM model contextually leverages the potentialities of optimized SPTN, extracts high-level features, and effectively classifies fish species using the EKM classifier. The experimental investigation of the proposed SPTN-EKM and the baseline fish species recognition model is conducted using two publicly available datasets, namely, Fish-Pak and QUT datasets, and a synthetic dataset called the Cephalopod dataset, which includes images of fish species found in the Kasimedu and Tuticorin coastal areas of the Bay of Bengal. The experimental outcomes of the proposed SPTN-EKM model with respect to Fish-Pak, QUT, and Cephalopod datasets confirm an increased accuracy of 98.61%, 96.34% and 93.34% respectively, for samples considered for recognition. It is also identified to significantly minimize the training time compared to the baseline DL-based models considered for fish species recognition.