What do you call a group of similar organisms that can breed and produce fertile offspring?

The correct term for a group of similar organisms that can breed and produce fertile offspring is "species." In biological classification, species are the basic unit of taxonomy and represent a group of individuals that share common characteristics and genetic makeup. Additionally, members of the same species can interbreed successfully under natural conditions, leading to viable and fertile offspring. This ability to reproduce and maintain genetic continuity is what defines a species.

In contrast, "genus" is a higher taxonomic category that encompasses one or more species, while "family" is even broader, grouping multiple genera. "Order" is a further classification that includes various families. Thus, "species" is the most specific classification directly related to the ability to reproduce and produce fertile offspring.