There are not many large medical image datasets available. For these datasets, too small deep learning models can't learn useful features, so they don't work well due to underfitting, and too big models tend to overfit the limited data. As a result, there is a compromise between the two issues. This paper proposes a training strategy Medi-CAT to overcome the underfitting and overfitting phenomena in medical imaging datasets. Specifically, the proposed training methodology employs large pre-trained vision transformers to overcome underfitting and adversarial and contrastive learning techniques to prevent overfitting. The proposed method is trained and evaluated on four medical image classification datasets from the MedMNIST collection. Our experimental results indicate that the proposed approach improves the accuracy up to 2% on three benchmark datasets compared to well-known approaches, whereas it increases the performance up to 4.1% over the baseline methods.