Final answer:
The most specific classification category for organisms is the species, which represents a group capable of interbreeding and producing fertile offspring. It is the final and most precise category in the Linnaean system of taxonomic classification.
Step-by-step explanation:
The most specific group used to classify organisms within the modern taxonomic classification system is the species. This system, also known as the Linnaean system after its inventor Carl Linnaeus, organizes life forms into a hierarchy from the least specific to the most specific categories. The order from the broadest to the most specific is: domain, kingdom, phylum, class, order, family, genus, and species. The species is the most precisely defined category, representing a group of organisms that can interbreed and produce fertile offspring. Under the binomial nomenclature system, each species has a unique two-part scientific name consisting of its genus and species designations, such as in Homo sapiens, where 'Homo' is the genus and 'sapiens' is the species.