Background Some studies show an association between the apolipoprotein E epsilon 4 allele (ApoE epsilon 4) and obstructive sleep apnea syndrome (OSAS), and other studies, an association between ApoE epsilon 4 and excessive daytime sleepiness (EDS), but there are no data in the literature on the interaction between EDS, cognitive function, and ApoE epsilon 4 in patients with OSA. Objective To examine the cognitive function of adults with and without EDS and with and without ApoE epsilon 4.Methods A total of 21 male and female patients aged between 33 and 79 years, underwent a clinical interview, ApoE genotyping, neuropsychological evaluation, polysomnography, and the application of the Epworth Sleepiness Scale. Results Excessive daytime sleepiness was associated with lower intelligence quotient (IQ; total performance) and worse immediate visual memory, regardless of the ApoE genotype. Patients carrying the ApoE epsilon 3/epsilon 4 genotype had a worse performance in divided attention, constructional praxis, perceptual organization, and cognitive flexibility. A combination of the epsilon 4 allele and EDS potentiates the negative effect on cognition, except for immediate visual memory. In this case, patients had a worse performance in terms of processing speed, selective attention, and visuomotor coordination. Conclusions Excessive daytime sleepiness and the ApoE epsilon 3/epsilon 4 genotype are associated with worse cognitive performance in OSA patients. The combination of EDS and epsilon 4 allele potentiates cognitive impairment.