Both shared and unique genetic risk factors underlie the two symptom domains of attention deficit hyperactivity disorder (ADHD): inattention and hyperactivity-impulsivity. The developmental course and relationship to co-occurring disorders differs across the two symptom domains, highlighting the importance of their partially distinct etiologies. Familial cognitive impairment factors have been identified in ADHD, but whether they show specificity in relation to the two ADHD symptom domains remains poorly understood. We aimed to investigate whether different cognitive impairments are genetically linked to the ADHD symptom domains of inattention versus hyperactivity-impulsivity. We conducted multivariate genetic model fitting analyses on ADHD symptom scores and cognitive data, from go/no-go and fast tasks, collected on a population twin sample of 1,312 children aged 7-10. Reaction time variability (RTV) showed substantial genetic overlap with inattention, as observed in an additive genetic correlation of 0.64, compared to an additive genetic correlation of 0.31 with hyperactivity-impulsivity. Commission errors (CE) showed low additive genetic correlations with both hyperactivity-impulsivity and inattention (genetic correlations of 0.17 and 0.11, respectively). The additive genetic correlation between RTV and CE was also low and non-significant at -0.10, consistent with the etiological separation between the two indices of cognitive impairments. Overall, two key cognitive impairments phenotypically associated with ADHD symptoms, captured by RTV and CE, showed different genetic relationships to the two ADHD symptom domains. The findings extend a previous model of two familial cognitive impairment factors in combined subtype ADHD by separating pathways underlying inattention and hyperactivity-impulsivity symptoms.