Background Genome‐wide association studies in adults have identified numerous genetic variants related to psychiatric disorders and related traits, such as schizophrenia and educational attainment. However, the effects of these genetic variants on behaviour in the general population remain to be fully understood, particularly in younger populations. We investigated whether polygenic scores of five psychiatric disorders and educational attainment are related to emotional and behaviour problems during early childhood. Methods From the Generation R Study, we included participants with available genotype data and behavioural problems measured with the Child Behavior Checklist (CBCL) at the age of 3 (n = 1,902), 6 (n = 2,202) and 10 years old (n = 1,843). Polygenic scores were calculated for five psychiatric disorders and educational attainment. These polygenic scores were tested for an association with the broadband internalizing and externalizing problem scales and the specific CBCL syndrome scale scores. Results Analysis of the CBCL broadband scales showed that the schizophrenia polygenic score was associated with significantly higher internalizing scores at 3, 6 and 10 years and higher externalizing scores at age 3 and 6. The educational attainment polygenic score was associated with lower externalizing scores at all time points and lower internalizing scores at age 3. No associations were observed for the polygenic scores of bipolar disorder, major depressive disorder and autism spectrum disorder. Secondary analyses of specific syndrome scores showed that the schizophrenia polygenic score was strongly related to the Thought Problems scores. A negative association was observed between the educational attainment polygenic score and Attention Problems scores across all age groups. Conclusions Polygenic scores for adult psychiatric disorders and educational attainment are associated with variation in emotional and behavioural problems already at a very early age.