Leukemia is a fatal category of cancer-related disease that affects individuals of all ages, including children and adults, and is a significant cause of death worldwide. Particularly, it is associated with White Blood Cells (WBC), which is accompanied by a rise in the number of immature lymphocytes and cause damage to the bone marrow and/or blood. Therefore, a rapid and reliable cancer diagnosis is a critical requirement for successful therapy to raise survival rates. Currently, a manual analysis of blood samples obtained through microscopic images is done to diagnose this disease, which is often very slow, time-consuming, and less accurate. Furthermore, in microscopic analysis, the appearance and shape of leukemic cells seem very similar to normal cells which make detection more difficult. In the past decades, deep learning utilizing Convolutional Neural Networks (CNN) has provided state-of-the-art approaches for image classification problems; however, there is still a gap to improve their efficacy, learning procedure, and performance. Therefore, in this research study, we proposed a new variant of deep learning algorithm to diagnose leukemia disease by analyzing the microscopic images of blood samples. The proposed deep learning architecture emphasizes the channel associations on all levels of feature representation by incorporating the squeeze and excitation learning that recursively performs recalibration on channel-wise feature outputs by modeling channel interdependencies explicitly. In addition, the incorporation of the squeeze-and-excitation process enhances the feature discriminability of leukemic and normal cells, and strategically assists in exposing informative features of leukemia cells while suppressing less valuable ones as well as improving feature representational power of deep learning algorithm. We show that piling these learning operations of squeeze and excite together in a deep learning model can improve the performance of the model in diagnosing leukemia from microscopic images based on blood samples of patients. Furthermore, an extensive set of experiments are performed on both cropped cells and full-size microscopic images as well as with data augmentation to address the problem of fewer data and to further boost their performance. The proposed model is tested on two publicly available datasets of blood samples of leukemia patients, namely, ALL_IDB1 and ALL_IDB2. The suggested deep learning model exhibits good results and can be utilized to make a reliable computer-aided diagnosis for leukemia cancer.