Attention-deficit hyperactivity disorder (ADHD) is a neurodevelopmental disorder with onset in childhood (childhood ADHD); two-thirds of affected individuals continue to have ADHD in adulthood (persistent ADHD), and sometimes ADHD is diagnosed in adulthood (late-diagnosed ADHD). We evaluated genetic differences among childhood (n = 14,878), persistent (n = 1,473) and late-diagnosed (n = 6,961) ADHD cases alongside 38,303 controls, and rare variant differences in 7,650 ADHD cases and 8,649 controls. We identified four genome-wide significant loci for childhood ADHD and one for late-diagnosed ADHD. We found increased polygenic scores for ADHD in persistent ADHD compared with the other two groups. Childhood ADHD had higher genetic overlap with hyperactivity and autism compared with late-diagnosed ADHD and the highest burden of rare protein-truncating variants in evolutionarily constrained genes. Late-diagnosed ADHD had a larger genetic overlap with depression than childhood ADHD and no increased burden in rare protein-truncating variants. Overall, these results suggest a genetic influence on age at first ADHD diagnosis, persistence of ADHD and the different comorbidity patterns among the groups.