Machine learning, with its myriad applications, has become an integral component of numerous technological systems. A common practice in this domain is the use of transfer learning, where a pre-trained model's architecture, readily available to the public, is fine-tuned to suit specific tasks. As Machine Learning as a Service (MLaaS) platforms increasingly use pre-trained models in their backends, it's crucial to safeguard these architectures and understand their vulnerabilities. In this work, we present an approach based on the observation that the classification patterns of adversarial images can be used as a means to steal the models. Furthermore, the adversarial image classifications in conjunction with timing side channels can lead to a model stealing method. Our approach, designed for typical user-level access in remote MLaaS environments exploits varying misclassifications of adversarial images across different models to fingerprint several renowned Convolutional Neural Network (CNN) and Vision Transformer (ViT) architectures. We utilize the profiling of remote model inference times to reduce the necessary adversarial images, subsequently decreasing the number of queries required. We have presented our results over 27 pre-trained models of different CNN and ViT architectures using CIFAR-10 dataset and demonstrate a high accuracy of 88.8% while keeping the query budget under 20.