The most common definition for a species is whether they can breed and produce fertile offspring. Thus all domestic dogs are the same species because they can produce offspring, excluding some ones with size complications like St. Bernards and chihuahuas. With DNA testing it appears that modern humans and Neaderthals did breed when they met.
I’ve seen research that indicates that the offspring of modern human/Neanderthal pairings weren’t as robust as their parents, which could explain the low amount of Neanderthal DNA in our own genes, i.e., 2%.
Apparently relatively few offspring survived and successfully bred.
Maybe just at the border of being the same species.