Background: Sleep patterns, including daytime napping and nighttime sleep duration, have complex relationships with cognitive health, yet the nonlinear associations across diverse populations remain underexplored. Methods: Utilizing harmonized cognitive assessment protocol from the China Health and Retirement Longitudinal Study (CHARLS-HCAP) and the Survey of Health, Ageing, and Retirement in Europe(SHARE-HCAP). Cognitive function was assessed based on Minimum Mental State Examination (MMSE), Brief Community Screening Instrument-Dementia (BCSID,10/66). Cognitive domains included orientation, memory, visuospatial, executive, and language function, measured via several protocols such as Consortium to Establish a Registry for Alzheimer's Disease (CERAD), Trail Making Test A/B (TMT-A/B), number series and Symbol Digit Modalities Test (SDMT). Restricted cubic spline (RCS) models and multivariate regression were applied to assess the threshold effect. Results: In CHARLS, 4307 subjects were included and 2685 in SHARE. Chinese older adults napping rate is 66 % versus 31.51 % in Europe. In CHARLS, napping exhibited an inverted U-shaped relationship with cognitive function, with optimal nap duration at 42-50 min and sleep duration of 5.8-7 h. Although exhibiting similar inverted U-shaped trends, SHARE demonstrated distinct sleep pattern effects on cognition, particularly nap duration (35-40 min for naps; 6-6.7 h for sleep). Cross-regional studies reveal cognitively friendly sleep pattern, with Chinese older adults napping for 35-60 min and sleeping for 5-7 h, and European napping for 5-75 min, sleeping for 4-8 h. Conclusions: Both napping and sleep duration exhibit nonlinear, domain-specific relationships with cognitive performance. Public health guidelines should emphasize association between sleep patterns and cognitive performance in older adults, with attention to the impact of lifestyle habits.