BACKGROUND: Simple and affordable methods for evaluating Insulin Resistance (IR) have been suggested, such as the Triglyceride-Glucose (TyG) index and its variants, including the TyG-Body Mass Index (TyG-BMI), TyG-Waist Circumference (TyG-WC), and TyG-Waist-to-Height Ratio (TyG-WHtR). The aim of this study is to investigate the relationship between these TyG-related indices, which measure IR, and Obstructive Sleep Apnea (OSA). METHODS: This study analyzed NHANES data from 2007-2008, 2015-2016, and 2017-2020. TyG and its derivatives were evaluated as continuous and categorical variables in relation to OSA using multivariable logistic regression models. Subgroup analyses, dose-response relationships, and threshold effects were explored, and the diagnostic performance of TyG-related indices was assessed using AUC curves. RESULTS: The study included 8,374 participants. The fully adjusted Model 3 analysis (Note: Body Mass Index was not adjusted for TyG-BMI) of continuous variables showed a positive correlation between OSA and all four indices. All four TyG-related indicators showed statistically significant relationships with OSA when grouped into quartiles (TyG: AOR = 1.448, 95% CI: 1.260-1.663; TyG-BMI: AOR = 3.785, 95% CI: 3.319-4.317; TyG-WC: AOR = 2.089, 95% CI: 1.629-2.677; TyG-WHtR: AOR = 1.913, 95% CI: 1.548-2.363). Subgroup analysis revealed a stronger association of TyG-WHtR with OSA in the 41-59 age group (AOR = 1.459, 95% CI: 1.254-1.698) and the low-income group (AOR = 1.451, 95% CI: 1.241-1.698). TyG showed a linear relationship with OSA, while TyG-BMI, TyG-WC, and TyG-WHtR exhibited nonlinear relationships. The diagnostic capability was highest for TyG-WC, with an AUC of 0.647. CONCLUSION: The study confirms strong associations between OSA and the TyG indices, particularly TyG-WC, which demonstrates significant predictive power for OSA risk. Future longitudinal studies are recommended to further investigate these associations and enhance OSA management in resource-constrained environments.