In the pursuit of personalized medicine, the development of efficient, cost-effective, and reliable DNA sequencing technology is crucial. Nanotechnology, particularly the exploration of two-dimensional materials, has opened different avenues for DNA nucleobase detection, owing to their impressive surface-to-volume ratio. This study employs density functional theory with van der Waals corrections to methodically scrutinize the adsorption behavior and electronic band structure properties of a DNA system composed of eight hachimoji nucleotide letters adsorbed on both MoS and MoSSe monolayers. Through a comprehensive conformational search, we pinpoint the most favorable adsorption sites, quantifying their adsorption energies and charge transfer properties. The analysis of electronic band structure unveils the emergence of flat bands in close proximity to the Fermi level post-adsorption, a departure from the pristine MoS and MoSSe monolayers. Furthermore, leveraging the nonequilibrium Green's function approach, we compute the current-voltage characteristics, providing valuable insights into the electronic transport properties of the system. All hachimoji bases exhibit physisorption with a horizontal orientation on both monolayers. Notably, base G demonstrates high sensitivity on both substrates. The obtained current-voltage (-) characteristics, both without and with base adsorption on MoS and the Se side of MoSSe, affirm excellent sensing performance. This research significantly advances our understanding of potential DNA sensing platforms and their electronic characteristics, thereby propelling the endeavor for personalized medicine through enhanced DNA sequencing technologies.