Objective: To explore the impact of intergenerational connections on cognitive function in middle-aged and older adults (45-60 years and over 60 years, respectively) and analyze the urban-rural and sex differences in the effects of intergenerational connections on cognitive function., Method: Based on China Health and Retirement Longitudinal Study data (CHARLS), this study conducted ID matching for four waves of data from 2011, 2013, 2015, and 2018. Cognitive function was measured via Telephone Interview for Cognitive Status-modified (TICS-m), word recall, and imitation drawing. Using a combination of cross-sectional and longitudinal research, we constructed the cross-lagged panel model (CLPM) with a sample of 1,480 participants to explore the relationship between intergenerational connections and cognitive function., Results: This study examines the impact of intergenerational connections on cognitive function in middle-aged (45-60 years) and older adults (over 60 years) using data from the CHARLS. It identifies urban-rural and sex differences, with notable effects among rural female participants. The frequency of meeting with one child negatively predicts cognitive function ( β = -0.040, p = 0.041), and the frequency of communication with one child positively predicts cognitive function ( β = 0.102, 0.068, 0.041, p < 0.001, p = 0.001, 0.045). Meanwhile, intergenerational connections with multiple children positively predicts cognitive function ( β = 0.044, p = 0.031), ( β = 0.128, 0.084, and 0.056, p < 0.001, 0.001, p = 0.008). There are urban-rural and sex differences in the effects of intergenerational connections on cognitive function; additionally, the effects of intergenerational connections on cognitive function are significant in rural female middle-aged and older adults., Discussion: This study proposes the theory of skewed intergenerational support, which suggests that as middle-aged and older adults age, the responsibility for intergenerational support is skewed toward one child. This leads to conflicts between middle-aged and older parents and the child, which further affects cognitive function. In addition, this study put forward the boat-carrying theory of intergenerational relations and "to hold a bowl of water level" is the art of dealing with intergenerational relationships., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Hu, Ge, Fang and Yang.)