Single-cell omics technologies enable molecular characterization of diverse cell types and states, but how the resulting transcriptional and epigenetic profiles depend on the cell’s genetic background remains understudied. We describe Monopogen, a computational tool to detect single-nucleotide variants (SNVs) from single-cell sequencing data. Monopogen leverages linkage disequilibrium from external reference panels to identify germline SNVs and detects putative somatic SNVs using allele cosegregating patterns at the cell population level. It can identify 100 K to 3 M germline SNVs achieving a genotyping accuracy of 95%, together with hundreds of putative somatic SNVs. Monopogen-derived genotypes enable global and local ancestry inference and identification of admixed samples. It identifies variants associated with cardiomyocyte metabolic levels and epigenomic programs. It also improves putative somatic SNV detection that enables clonal lineage tracing in primary human clonal hematopoiesis. Monopogen brings together population genetics, cell lineage tracing and single-cell omics to uncover genetic determinants of cellular processes.