Single-cell transcriptome data can provide insights into how genetic variation influences biological processes involved in human biology and disease. However, the identification of gene-level associations in distinct cell types faces several challenges, including the limited reference resource from population scale studies, data sparsity in single-cell RNA sequencing, and the complex cell-state pattern of expression within individual cell types. Here we develop genetic models of cell type specific and cell state adjusted gene expression in mid-brain neurons in the process of specializing from induced pluripotent stem cells. The resulting framework quantifies the dynamics of the genetic regulation of gene expression and estimates its cell type specificity. As an application, we show that the approach detects known and new genes associated with schizophrenia and enables insights into context-dependent disease mechanisms. We provide a genomic resource from a phenome-wide application of our models to more than 1500 phenotypes from the UK Biobank. Using longitudinal genetically determined expression, we implement a predictive causality framework, evaluating the prediction of future values of a target gene expression using prior values of a putative regulatory gene. Collectively, this work demonstrates the insights that can be gained into the molecular underpinnings of diseases by quantifying the genetic control of gene expression at single-cell resolution.