Background <p>Obstructive sleep apnoea (OSA), Non-alcoholic fatty liver disease (NAFLD) and insulin resistance (IR) are interlinked. The aim of our study was to investigate the predictive value of metabolic score for insulin resistance (METS-IR) and triglyceride-glucose(TyG) index in relation to OSA combined with NAFLD in physical examination population.</p> Methods <p>This is a retrospective observational study. 329 physical examiners who attended the healthcare centre of the First Affiliated Hospital of Wenzhou Medical University for polysomnography and abdominal ultrasonography (or CT abdominal scanning) from September 2021 to July 2024. Subjects were categorized into two groups according to the presence or absence of combined NAFLD. Logistic regression analysis and restricted cubic spline model (RCS) were used to evaluate the relationship between TyG index and METS-IR and NAFLD. The predictive value of TyG index and METS-IR for NAFLD was determined by receiver operating characteristic curves (ROC curves).</p> Results <p>A total of 329 subjects were analyzed. The prevalence of NAFLD increased with increasing TyG index (P for trend &lt; 0.001), and METS-IR showed an increasing–decreasing-increasing trend with NAFLD risk (P for trend &lt; 0.001). RCS analysis showed a dose–response relationship between NAFLD risk and METS-IR (<i>p</i> = 0.012) and a linear relationship with the TyG index (<i>p</i> = 0.078), with a significant increase in the risk of NAFLD when the METS-IR exceeded a threshold of 47.47 (OR = 1). Compared with TyG index (AUC = 0.775, 95% CI: 0.711–0.828), METS-IR (AUC = 0.778, 95% CI: 0.716–0.836) had a higher predictive value for NAFLD in the OSA physical examination population.</p> Conclusions <p>In the OSA population, TyG index and METS-IR had predictive value for the development of NAFLD, with METS-IR being superior to TyG index.</p>