Background: Few studies found that obstructive sleep apnea (OSA) may be related to postoperative neurocognitive disorders (PND) including postoperative delirium (POD) and cognitive decline (POCD) in the early postoperative period. However, the results are controversial and need further verification, and no research has explored the effect of OSA on the incidence of PND during the 1-year follow-up periods. Furthermore, OSA patients with excessive daytime sleepiness (EDS) as a severe phenotype have more significant neurocognitive impairments, but the relationship between OSA with EDS and PND within 1 year after surgery has not been studied. Objectives: To explore the effect of moderate-to-high risk of OSA and the moderate-to-high risk of OSA with EDS on PND within 1 year after surgery. Methods: In this prospective cohort study, including 227 older patients, moderate-to-high risk of OSA (using STOP-BANG), subjective EDS (using Epworth Sleepiness Scale), and objective EDS (using Actigraphy) were selected as exposures. Key outcomes included POD during hospitalization (using Confusion Assessment Method-Severity), POCD at discharge, 1-month and 1-year after surgery (using Mini-Mental State Examination and Telephone Interview for Cognitive Status-40). We applied multiple logistic regression models to estimate the effect of moderate-to-high risk of OSA and moderate-to-high risk of OSA with EDS on PND. Results: In the multivariate analysis, moderate-to-high risk of OSA was not associated with POD during hospitalization and POCD at discharge, 1-month, and 1-year after surgery (p > 0.05). However, the moderate-to-high risk of OSA with subjective EDS was related to POCD at discharge compared to the moderate-to-high risk of OSA or normal group (no moderate-to-high risk of OSA and no EDS) (p < 0.05). In addition, moderate-to-high risk of OSA with objective EDS was associated with POCD at discharge, 1-month, and 1-year postoperatively compared to the moderate-to-high risk of OSA or normal group (p < 0.05). Conclusion: Moderate-to-high risk of OSA with EDS, not moderate-to-high risk of OSA alone, was a clinically helpful predictor for POCD within 1-year after surgery and should be routinely assessed before surgery.