Associations of Physical Fitness with Cognitive Performance in Children Aged 7–12 Years: A Cross-Sectional Study

(1) Background: The objective of the present study was to analyze the association of physical fitness, specifically lower limb strength, abdominal strength, vertical jump, and grip strength, with cognitive performance, specifically focusing on selective attention and memory in children aged 7 to 12 years. (2) Methods: Two hundred twenty-seven students participated in this study. Pearson correlation was used to analyze potential relationships between the independent variables and dependent variables. (3) Results: In relation to physical fitness, a higher number of abdominal repetitions performed in 30 s showed a significant and positive association with a higher number of correct responses assessed by the Stroop Test. Furthermore, at a functional level, higher grip strength correlated with a greater number of correct responses and a higher average correct response time in the Stroop Test. Additionally, grip strength showed a significant and positive correlation with the number of words recalled assessed by the word recall test. Our key findings showed a significant association of grip strength with the categories of cognitive status, selective attention, and memory. (4) Conclusions: This study reveals that physical fitness levels, especially grip strength and abdominal strength, correlate with selective attention capacity in primary school students.