The Internet of Medical Things (IoMT) is poised to play a pivotal role in future medical support systems, enabling pervasive health monitoring in smart cities. Alzheimer's disease (AD) afflicts millions globally, and this paper explores the potential of electroencephalogram (EEG) data in addressing this challenge. We propose the Convolutional Learning Attention-Bidirectional Time-Aware Long-Short-Term Memory (CL-ATBiLSTM) model, a deep learning approach designed to classify different AD phases through EEG data analysis. The model utilizes Discrete Wavelet Transform (DWT) to decompose EEG data into distinct frequency bands, allowing for targeted analysis of AD-related brain activity patterns. Additionally, the data is segmented into smaller windows to handle the dynamic nature of EEG signals, and these segments are transformed into spectrogram images, visually depicting brain activity distribution over time and frequency. The CL-ATBiLSTM model incorporates convolutional layers to capture spatial features, attention mechanisms to emphasize crucial data, and BiLSTM networks to explore temporal relationships within the sequences. To optimize the model's performance, Bayesian optimization is employed to fine-tune the hyperparameters of the ATBiLSTM network, enhancing its ability to generalize and accurately classify AD stages. Incorporating Bayesian learning ensures the most effective model configuration, improving sensitivity and specificity for identifying AD-related patterns. Our model extracts discriminative features from EEG data to differentiate between AD, Mild Cognitive Impairment (MCI), and healthy controls (CO), offering a more comprehensive approach than existing two-class detection algorithms. By including the MCI category, our method facilitates earlier identification and potentially more impactful therapy interventions. Achieving a 96.52% accuracy on Figshare datasets containing AD, MCI, and CO groups, our approach demonstrates strong potential for practical use, accelerating AD identification, enhancing patient care, and contributing to the development of targeted treatments for this debilitating condition.