Lack of diversity in human genomics limits our understanding of the genetic underpinnings of complex traits, hinders precision medicine, and contributes to health disparities. To map genetic effects on gene regulation in the underrepresented Indonesian population, we have integrated genotype, gene expression, and CpG methylation data from 115 participants across three island populations that capture the major sources of genomic diversity in the region. In a comparison with European datasets, we identify eQTLs shared between Indonesia and Europe as well as population-specific eQTLs that exhibit differences in allele frequencies and/or overall expression levels between populations. By combining local ancestry and archaic introgression inference with eQTLs and methylQTLs, we identify regulatory loci driven by modern Papuan ancestry as well as introgressed Denisovan and Neanderthal variation. GWAS colocalization connects QTLs detected here to hematological traits, and further comparison with European datasets reflects the poor overall transferability of GWAS statistics across diverse populations. Our findings illustrate how population-specific genetic architecture, local ancestry, and archaic introgression drive variation in gene regulation across genetically distinct and in admixed populations and highlight the need for performing association studies on non-European populations.