Genome-scale datasets are resolving challenging nodes across the tree of life. These datasets, however, characterized by inherent heterogeneity, often push traditional phylogenetic reconstruction methods to their limits. By integrating multiple phylogenomic approaches, we can identify the causes of topological discordance within genomic partitions while accounting for various sources of heterogeneity and systematic errors. Here we conduct the first in-depth analysis of discordance for the reef family Pomacanthidae (marine angelfishes) using target enrichment data of ~1,000 ultraconserved elements from 45 pomacanthid species. Our combined phylogenomic approach resolved the systematics of the family at the base of the pomacanthid tree. Despite this resolution, our analyses also highlight discordance in ancestral nodes associated with the paraphyletic Centropyge genus and monotypic Pygoplites lineage, and the impact of incomplete lineage sorting in the evolutionary history of pomacanthids. Species network searches and model selection supported a reticulated evolutionary history, suggesting three ancient gene flow events between ghost (or unsampled) lineages at the root of the Pomacanthidae tree and ancestors of Genicanthus, Centropyge, Chaetodontoplus, and Pomacanthus lineages. This study advances our understanding of diagnosing topological discordance in genome-scale phylogenies and provide an analytical pathway for limiting systematic errors. In the process of diagnosing discordance, we identify key evolutionary processes involved in the complex evolution of marine angelfishes. While often inconvenient in phylogenetic analyses, patterns of discordance can shed light on underlying biological and evolutionary processes that shape the evolution of biodiversity.