Identification of specific species in metagenomic samples is critical for several key applications, yet many tools available require large computational power and are often prone to false positive identifications. Here we describe High-AccuracY and Scalable Taxonomic Assignment of MetagenomiC data (HAYSTAC), which can estimate the probability that a specific taxon is present in a metagenome. HAYSTAC provides a user-friendly tool to construct databases, based on publicly available genomes, that are used for competitive read mapping. It then uses a novel Bayesian framework to infer the abundance and statistical support for each species identification and provide per-read species classification. Unlike other methods, HAYSTAC is specifically designed to efficiently handle both ancient and modern DNA data, as well as incomplete reference databases, making it possible to run highly accurate hypothesis-driven analyses (i.e., assessing the presence of a specific species) on variably sized reference databases while dramatically improving processing speeds. We tested the performance and accuracy of HAYSTAC using simulated Illumina libraries, both with and without ancient DNA damage, and compared the results to other currently available methods (i.e., Kraken2/Bracken, KrakenUniq, MALT/HOPS, and Sigma). HAYSTAC identified fewer false positives than both Kraken2/Bracken, KrakenUniq and MALT in all simulations, and fewer than Sigma in simulations of ancient data. It uses less memory than Kraken2/Bracken, KrakenUniq as well as MALT both during database construction and sample analysis. Lastly, we used HAYSTAC to search for specific pathogens in two published ancient metagenomic datasets, demonstrating how it can be applied to empirical datasets. HAYSTAC is available from https://github.com/antonisdim/HAYSTAC.