Electroencephalography (EEG) emotion recognition signals have become one of the foundations of affective computing, enabling advancements in human-computer interaction, mental health diagnostics, and personalized user experiences. This paper presents CBSAtt, a deep learning architecture that synergistically merges Convolutional Neural Networks, Bidirectional Long Short-Term Memory (BiLSTM) networks, and multi-head self-attention mechanisms to classify emotions effectively. The proposed model uses pre-computed differential entropy features from the SEED-IV dataset, which is provided by the Center for Brain-like Computing and Machine Intelligence at the Department of Computer Science and Engineering, Shanghai Jiao Tong University, China. The dataset captures spectral information across five frequency bands from 62 EEG channels. Our architecture uses a 1D-Convolutional Neural Network to learn salient spatial features from the multidimensional input, followed by a BiLSTM to model long-range time-dependent dependencies. A multi-head self-attention layer is then used selectively on the most informative temporal segments, enhancing discriminative capability. The model is measured in a subject-dependent environment throughout all three sessions with the SEED-IV dataset, attaining an average accuracy of 95.50% with best-epoch checkpointing. This result demonstrates improved performance compared to transformer-based approaches such as AMDET (87.32%) on the same dataset, demonstrating the powerful synergy of convolutional, recurrent, and attentional mechanisms in decoding complex neural patterns associated with emotional states. Our findings provide a robust foundation for developing advanced affective brain-computer interfaces.