Multiancestry statistical fine-mapping of cis-molecular quantitative trait loci (cis-molQTL) aims to improve the precision of distinguishing causal cis-molQTLs from tagging variants. Here we present the sum of shared single effects (SuShiE) model, which leverages linkage disequilibrium heterogeneity to improve fine-mapping precision, infer cross-ancestry effect size correlations and estimate ancestry-specific expression prediction weights. Through extensive simulations, we find that SuShiE consistently outperforms existing methods. We apply SuShiE to 36,907 molecular phenotypes including mRNA expression and protein levels from individuals of diverse ancestries in the TOPMed-MESA and GENOA studies. SuShiE fine-maps cis-molQTLs for 18.2% more genes compared with existing methods while prioritizing fewer variants and exhibiting greater functional enrichment. While SuShiE infers highly consistent cis-molQTL architectures across ancestries, it finds evidence of heterogeneity at genes with predicted loss-of-function intolerance. Lastly, using SuShiE-derived cis-molQTL effect sizes, we perform transcriptome- and proteome-wide association studies on six white blood cell-related traits in the All of Us biobank and identify 25.4% more genes compared with existing methods. Overall, SuShiE provides new insights into the cis-genetic architecture of molecular traits.