Generative models, especially Diffusion Models, have demonstrated remarkable capability in generating high-quality synthetic data, including medical images. However, traditional class-conditioned generative models often struggle to generate images that accurately represent specific medical categories, limiting their usefulness for applications such as skin cancer diagnosis. To address this problem, we propose a classification-induced diffusion model, namely, Class-N-Diff, to simultaneously generate and classify dermoscopic images. Our Class-N-Diff model integrates a classifier within a diffusion model to guide image generation based on its class conditions. Thus, the model has better control over class-conditioned image synthesis, resulting in more realistic and diverse images. Additionally, the classifier demonstrates improved performance, highlighting its effectiveness for downstream diagnostic tasks. This unique integration in our Class-N-Diff makes it a robust tool for enhancing the quality and utility of diffusion model-based synthetic dermoscopic image generation. Our code is available at https://github.com/Munia03/Class-N-Diff.