Alzheimer's disease (AD) is a common neurodegenerative disorder, currently lacking effective early diagnostic methods. However, natural killer (NK) cells may play a potential role in AD pathogenesis. This study aims to identify AD-related feature genes from NK cell markers to construct a diagnostic model and explore their potential biological mechanisms in AD. Single-cell RNA sequencing data was used to identify NK cell markers. A novel feature selection algorithm, adaptive dynamic graph convolutional network (ADGCN), was proposed to extract AD-related feature genes and construct a diagnostic model. Differential, correlation and enrichment analyses were performed to understand the biological mechanisms of these genes. Immune infiltration analysis compared the immune microenvironment between AD and controls. Two regulatory networks explored interactions between feature genes, transcription factors and microRNAs. The association between SNPs and feature genes' expression was examined through expression quantitative trait loci analysis. Differential CpG sites were identified to analyze their association with the NK cell markers' expression. We developed an optimal diagnostic model (ADGCN-XGBoost) with 17 feature genes, demonstrating high diagnostic effectiveness across datasets. These genes were primarily related to macromolecule biosynthesis, cytoplasmic translation biological processes and ribosome pathway, and potentially modulated immune infiltration of AD patients. We predicted 27 target miRNAs and 21 transcription factors influencing these genes. Multimodal analysis identified 57 significant SNP-gene associations and seven CpG-gene pairs. This study proposed a novel feature selection algorithm and developed a diagnostic model based on 17 feature genes, providing new potential biomarkers for AD diagnosis.