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Stromal antigen 1 (STAG1), a component of cohesion, is overexpressed in various cancers, but it is unclear whether it has a role in the transcriptional regulation of hepatocellular carcinoma (HCC). To test this hypothesis, here, we screened global HCC datasets and performed multiscale embedded gene co‐expression network analysis to identify the potential functional modules of differentially expressed STAG1 co‐expressed genes. The putative transcriptional targets of STAG1 were identified using chromatin immunoprecipitation followed by high‐throughput DNA sequencing. The cohesin‐associated gene score (CAGS) was quantified using the The Cancer Genome Atlas HCC cohort and single‐sample gene set enrichment analysis. Distinct cohesin‐associated gene patterns were identified by calculating the euclidean distance of each patient. We assessed the potential ability of the CAGS in predicting immune checkpoint blockade (ICB) treatment response using IMvigor210 and GSE78220 cohorts. STAG1 was upregulated in 3313 HCC tissue samples compared with 2692 normal liver tissue samples (standard mean difference = 0.54). A total of three cohesin‐associated gene patterns were identified, where cluster 2 had a high TP53 mutated rate and a poor survival outcome. Low CAGS predicted a significant survival advantage but presaged poor immunotherapy response. Differentially expressed STAG1 co‐expression genes were enriched in the mitotic cell cycle, lymphocyte activation, and blood vessel development. PDS5A and PDGFRA were predicted as the downstream transcriptional targets of STAG1. In summary, STAG1 is significantly upregulated in global HCC tissue samples and may participate in blood vessel development and the mitotic cell cycle. A cohesin‐associated gene scoring system may have potential to predict the ICB response.