Background A child's gender and ordinal position within a family have varied implications on his or her personality and cognitive development. However, little is known about whether or not parental educational level may moderate the effects of birth order and gender. Methods Basic Competence Test (BCT) scores of 290 588 young adolescents aged 15–16 years in Taiwan were analysed. Parental educational level was calculated as the highest educational attainment of the subjects’ parents. The multiple linear regression model was used to assess the modification effects of parental educational levels on the associations of interest. Results After controlling for covariates, we noted a clear inverse relationship between birth order and BCT scores in Mandarin, Mathematics and Science. Additionally, boys had significantly lower mean scores in Mandarin, but had significantly higher mean scores in both Mathematics and Science. We also found the significant interactive effects of birth order, gender and parental educational attainment on BCT scores, in which the birth order and gender effects were more evident in higher‐educated families than in lower‐educated ones. Conclusions This large cohort study confirmed that both birth order and gender may pose independent influences on BCT scores; moreover, such influences are significantly modified by parental educational attainment.