Genome-wide association studies (GWAS) for obstructive sleep apnoea (OSA) are limited due to the underdiagnosis of OSA, leading to misclassification of OSA, which consequently reduces statistical power. We performed a GWAS of OSA in the Million Veteran Program (MVP) of the U.S. Department of Veterans Affairs (VA) healthcare system, where OSA prevalence is close to its true population prevalence. We performed GWAS of 568,576 MVP participants, stratified by biological sex and by harmonized race/ethnicity and genetic ancestry (HARE) groups of White, Black, Hispanic, and Asian individuals. We considered both BMI adjusted (BMI-adj) and unadjusted (BMI-unadj) models. We replicated associations in independent datasets, and analysed the heterogeneity of OSA genetic associations across HARE and sex groups. We finally performed a larger meta-analysis GWAS of MVP, FinnGen, and the MGB Biobank, totalling 916,696 individuals. MVP participants are 91% male. OSA prevalence is 21%. In MVP there were 18 and 6 genome-wide significant loci in BMI-unadj and BMI-adj analyses, respectively, corresponding to 21 association regions. Of these, 17 were not previously reported in association with OSA, and 13 replicated in FinnGen (False Discovery Rate p-value < 0.05). There were widespread significant differences in genetic effects between men and women, but less so across HARE groups. Meta-analysis of MVP, FinnGen, and MGB biobank revealed 17 additional, previously unreported, genome-wide significant regions. Sex differences in genetic associations with OSA are widespread, likely associated with multiple OSA risk factors. OSA shares genetic underpinnings with several sleep phenotypes, suggesting shared aetiology and causal pathways. Described in acknowledgements.