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Spiking Neural Networks (SNNs) are attracting widespread interest due to their biological plausibility, energy efficiency, and powerful spatio-temporal information representation ability. Given the critical role of attention mechanisms in enhancing neural network performance, the integration of SNNs and attention mechanisms exhibits potential to deliver energy-efficient and high-performance computing paradigms. We present a novel Temporal-Channel Joint Attention mechanism for SNNs, referred to as TCJA-SNN. The proposed TCJA-SNN framework can effectively assess the significance of spike sequence from both spatial and temporal dimensions. More specifically, our essential technical contribution lies on: 1) We employ the squeeze operation to compress the spike stream into an average matrix. Then, we leverage two local attention mechanisms based on efficient 1D convolutions to facilitate comprehensive feature extraction at the temporal and channel levels independently. 2) We introduce the Cross Convolutional Fusion (CCF) layer as a novel approach to model the inter-dependencies between the temporal and channel scopes. This layer breaks the independence of these two dimensions and enables the interaction between features. Experimental results demonstrate that the proposed TCJA-SNN outperforms SOTA by up to 15.7% accuracy on standard static and neuromorphic datasets, including Fashion-MNIST, CIFAR10-DVS, N-Caltech 101, and DVS128 Gesture. Furthermore, we apply the TCJA-SNN framework to image generation tasks by leveraging a variation autoencoder. To the best of our knowledge, this study is the first instance where the SNN-attention mechanism has been employed for image classification and generation tasks. Notably, our approach has achieved SOTA performance in both domains, establishing a significant advancement in the field. Codes are available at https://github.com/ridgerchu/TCJA.