Genetic risk for autism spectrum disorder (ASD) is associated with hundreds of genes spanning a wide range of biological functions. The alterations in the human brain resulting from mutations in these genes remain unclear. Furthermore, their phenotypic manifestation varies across individuals. Here we used organoid models of the human cerebral cortex to identify cell-type-specific developmental abnormalities that result from haploinsufficiency in three ASD risk genes-SUV420H1 (also known as KMT5B), ARID1B and CHD8-in multiple cell lines from different donors, using single-cell RNA-sequencing (scRNA-seq) analysis of more than 745,000 cells and proteomic analysis of individual organoids, to identify phenotypic convergence. Each of the three mutations confers asynchronous development of two main cortical neuronal lineages-γ-aminobutyric-acid-releasing (GABAergic) neurons and deep-layer excitatory projection neurons-but acts through largely distinct molecular pathways. Although these phenotypes are consistent across cell lines, their expressivity is influenced by the individual genomic context, in a manner that is dependent on both the risk gene and the developmental defect. Calcium imaging in intact organoids shows that these early-stage developmental changes are followed by abnormal circuit activity. This research uncovers cell-type-specific neurodevelopmental abnormalities that are shared across ASD risk genes and are finely modulated by human genomic context, finding convergence in the neurobiological basis of how different risk genes contribute to ASD pathology.