Breast cancer is one of the worst illnesses, with a higher fatality rate among women globally. Breast cancer detection needs accurate mammography interpretation and analysis, which is challenging for radiologists owing to the intricate anatomy of the breast and low image quality. Advances in deep learning-based models have significantly improved breast lesions' detection, localization, risk assessment, and categorization. This study proposes a novel deep learning-based convolutional neural network (ConvNet) that significantly reduces human error in diagnosing breast malignancy tissues. Our methodology is most effective in eliciting task-specific features, as feature learning is coupled with classification tasks to achieve higher performance in automatically classifying the suspicious regions in mammograms as benign and malignant. To evaluate the model's validity, 322 raw mammogram images from Mammographic Image Analysis Society (MIAS) and 580 from Private datasets were obtained to extract in-depth features, the intensity of information, and the high likelihood of malignancy. Both datasets are magnificently improved through preprocessing, synthetic data augmentation, and transfer learning techniques to attain the distinctive combination of breast tumors. The experimental findings indicate that the proposed approach achieved remarkable training accuracy of 0.98, test accuracy of 0.97, high sensitivity of 0.99, and an AUC of 0.99 in classifying breast masses on mammograms. The developed model achieved promising performance that helps the clinician in the speedy computation of mammography, breast masses diagnosis, treatment planning, and follow-up of disease progression. Moreover, it has the immense potential over retrospective approaches in consistency feature extraction and precise lesions classification.