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Robots operating in human-centered environments, such as retail stores, restaurants, and households, are often required to distinguish between similar objects in different contexts with a high degree of accuracy. However, fine-grained object recognition remains a challenge in robotics due to the high intra-category and low inter-category dissimilarities. In addition, the limited number of fine-grained 3D datasets poses a significant problem in addressing this issue effectively. In this paper, we propose a hybrid multi-modal Vision Transformer (ViT) and Convolutional Neural Networks (CNN) approach to improve the performance of fine-grained visual classification (FGVC). To address the shortage of FGVC 3D datasets, we generated two synthetic datasets. The first dataset consists of 20 categories related to restaurants with a total of 100 instances, while the second dataset contains 120 shoe instances. Our approach was evaluated on both datasets, and the results indicate that it outperforms both CNN-only and ViT-only baselines, achieving a recognition accuracy of 94.50 % and 93.51 % on the restaurant and shoe datasets, respectively. Additionally, we have made our FGVC RGB-D datasets available to the research community to enable further experimentation and advancement. Furthermore, we successfully integrated our proposed method with a robot framework and demonstrated its potential as a fine-grained perception tool in both simulated and real-world robotic scenarios.