Single-cell RNA sequencing (scRNA-seq) is an advanced technology used to study cellular heterogeneity and diversity. It allows gene expression analysis at the single-cell level, but it also confronts several challenges, including high noise levels, high dimensionality, and high sparsity of data. These characteristics increase the difficulty of effectively clustering cells from scRNA-seq data. Therefore, we propose a new deep clustering approach, scAFC, specially designed for scRNA-seq data. This method combines an Autoencoder (AE) and a Graph Attention Network (GAT), where the AE is responsible for extracting key features from the data, and the GAT utilizes the relationships between cells to enhance feature expression. Through an innovative adaptive fusion module, we integrate the outputs of the AE and GAT at different levels and use an attention mechanism to dynamically adjust the contribution of different features. Furthermore, scAFC employs a self-supervised learning optimization module to refine the computation of clustering centers, effectively enhancing the clustering accuracy and the generalization ability of the model. Extensive testing on 12 public scRNA-seq datasets shows that the scAFC method not only improves clustering accuracy but also demonstrates superior performance in handling the complexity of single-cell data, outperforming some of the state-of-the-art scRNA sequencing clustering methods. Code: https://github.com/728267035/scAFC.git .