>>12654900If there are any "neanderthal" DNA in modern human population, it would be indistinguishable from any other DNA sources. Any significant enough cross breading will have happened over 500 generations ago, this is enough time to shuffle the genetic makeup of a population several times over.
Another problem is that if homo sapiens cross bred with neanderthals, this will leave our genes in them. If we find "their" genes in us, how can we be certain that is is not our genes that we find in them? Since the neanderthals have died out, rather slowly, the last few thousand years of their existence will have been one of a shrinking population and gene-pool.
Populations such as the neanderthal have probably mixed significantly with homo sapiens populations, and whatever we are today is more due to chance from population bottle necks such as disease, drought or famine.