Background: Polygenic risk scores (PRSs) operationalize genetic propensity toward a particular mental disorder and hold promise as early predictors of psychopathology, but before a PRS can be used clinically, explanatory power must be increased and the specificity for a psychiatric domain established. To enable early detection, it is crucial to study these psychometric properties in childhood. We examined whether PRSs associate more with general or with specific psychopathology in school-aged children. Additionally, we tested whether psychiatric PRSs can be combined into a multi-PRS score for improved performance. Methods: We computed 16 PRSs based on GWASs of psychiatric phenotypes, but also neuroticism and cognitive ability, in mostly adult populations. Study participants were 9,247 school-aged children from three population-based cohorts of the DREAM-BIG consortium: ALSPAC (UK), The Generation R Study (Netherlands), and MAVAN (Canada). We associated each PRS with general and specific psychopathology factors, derived from a bifactor model based on self-report and parental, teacher, and observer reports. After fitting each PRS in separate models, we also tested a multi-PRS model, in which all PRSs are entered simultaneously as predictors of the general psychopathology factor. Results: Seven PRSs were associated with the general psychopathology factor after multiple testing adjustment, two with specific externalizing and five with specific internalizing psychopathology. PRSs predicted general psychopathology independently of each other, with the exception of depression and depressive symptom PRSs. Most PRSs associated with a specific psychopathology domain, were also associated with general child psychopathology. Conclusions: The results suggest that PRSs based on current GWASs of psychiatric phenotypes tend to be associated with general psychopathology, or both general and specific psychiatric domains, but not with one specific psychopathology domain only. Furthermore, PRSs can be combined to improve predictive ability. PRS users should therefore be conscious of nonspecificity and consider using multiple PRSs simultaneously, when predicting psychiatric disorders.