Advancements in ancient DNA (aDNA) research have enabled the recovery of individual human genomes through target enrichment approaches. Despite the decreasing cost of next-generation sequencing, enrichment methods targeting single-nucleotide polymorphisms (SNPs) compiled in RNA/DNA hybrid panels remain costly and require further authentic optimisations. Here, we present the Tweap (Twist cheap) protocol as a cost-effective alternative to the commercialised Twist protocol for target enrichment via in-solution hybridisation of ancient human DNA by replacing the streptavidin-coated superparamagnetic beads for binding the hybridised targeted DNA. We evaluated the protocol on 14 double-stranded DNA libraries from ancient human individuals originating from a hot and humid climate zone known to accelerate DNA degradation. The selected individuals reflected similar preservation levels and a broad range of endogenous human DNA content (0.79-41.69%). We optimised and simplified both the Twist and Tweap protocols for target enrichment, particularly for libraries with ultra-low library complexity, making it reproducible in any life sciences laboratory. The modified Tweap protocol not only reduced overall reagent costs and consumption, contributing to more climate-conscious research, but also recovered up to 7% more unique SNPs when applying multi-pooling of libraries from the same individual. Our findings demonstrate that the Tweap protocol is a viable, efficient, and scalable alternative for SNP capture in ancient DNA (aDNA) studies, supporting broader accessibility and sustainability in ancient DNA research.