Background: Gene-environment interaction is likely to contribute to human development, but individual effects are difficult to detect, especially for behavioural outcomes. Genetic variants associated with phenotypic variability (i.e. those with heteroscedastic effects) are potential candidates for tests of interaction. We conduct the first study estimating genetic effects on phenotypic variability in childhood behavioural traits. Methods: We tested for genome-wide association of mean (mGWA) and variance (vGWA) effects for 71 behavioural traits across childhood (ages 6 months - 14 years) in the Norwegian Mother, Father and Child Birth Cohort Study (MoBa; NMEAN: 44,788; NMAX: 62,897). We estimated genetic effects on standardised factor scores (mean effects) and quantile integrated rank scores (variance effects). Independently associated loci were included in phenome-wide association analyses of publicly available GWA summary statistics. We also estimated the fraction of phenotypic variance accounted for by genome-wide mean and variance effects (heritability), as well as shared effects between childhood behavioural traits in MoBa (genetic correlations). Summary statistics from a selection of vGWA were used to compute variance-based polygenic scores (vPGS) in an independent sample, the Twins Early Development Study (NMAX=9,116). Scores were entered into regression models to test whether greater vPGS predicted greater phenotypic variability. Given that behavioural traits are known to be heterogeneous and difficult to measure, we performed parallel analyses with height and weight, to provide us with an additional comparison set. Results: Across the 71 behavioural phenotypes, there were 17 independent genetic variants associated with phenotypic variability, and 44 associated with mean levels. Overall, mean and variance effects were uncorrelated, but this varied between phenotypes. Genome-wide variance effects explained up to 9.7% of the variance (mean h2vGWA=1.8%), whereas mean effects explained up to 15.8% of the phenotypic variance (mean h2GWA=6.0%). In comparison, for height and weight variance effects explained up to 6.7% of the variance in phenotypic variability (mean h2vGWA=2.1%), and mean effects explained up to 42.7% of the phenotypic variance (mean h2GWA=30.5%). For a couple of traits, higher vPGS was associated with greater phenotypic variance (p<0.01), but associations were not consistent across traits, ages or statistical models. Discussion: We used a range of approaches to boost statistical power to detect effects and provide several candidate SNPs for follow-up analyses. Overall, there were fewer variance effects than mean effects, likely due to smaller effect sizes. This finding was mirrored across all levels of analysis. Detecting genetic effects and G×E involved in childhood psychological outcomes has proven difficult and will require larger samples. We provide an extensive summary of the phenotypes assessed in MoBa accompanied by GWA summary statistics made available for future meta-analyses.