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The interaction between T cell receptors (TCRs), peptides, and human leukocyte antigens (HLAs) underlies antigen-specific T cell immunity. Despite substantial advances in peptide-HLA presentation prediction, accurate modeling of coupled TCR-peptide-HLA recognition remains underdeveloped, limiting applications such as TCR and neoepitope prioritization in cancer and antigen identification in autoimmunity. Here we present StriMap, a unified framework for predicting TCR-peptide-HLA interactions by integrating physicochemical, sequence-context, and structural features at recognition interfaces. StriMap achieves state-of-the-art performance with improved generalizability and enables applications in both cancer and autoimmunity. As a case study in ankylosing spondylitis (AS), we screened 13 million peptides derived from 43,241 bacterial proteins and identified candidate molecular mimics that were experimentally validated to activate T cells expressing an AS-associated TCR. Notably, a top validated peptide was enriched in patients with inflammatory bowel disease (IBD), suggesting potential shared microbial triggers between AS and IBD. Overall, StriMap provides a generalizable framework for rational immunotherapy design and for dissecting antigenic drivers of autoimmunity.