As for as is known *now* (since there isn't that much Neandertal DNA with which to compare it), sub-Saharan Africans of the present day don't have any; eastern Asians have about 1/3 more than Europeans.
I always suspected my husband had Neanderthal DNA once I heard about the “ginger gene” and the fact that 40% of Scots and other northern British had it. I wouldn’t be surprised if he had more than 4%. He had red hair, clear light blue eyes, hairy body including one shoulder, heavy brow, crystalline hard teeth, extreme mesomorph physique, short legs, long torso, man’s growth at age 13, very strong for size (at 5’11” and 200 lbs was sparring partner for an Olympic heavyweight wrestling contender), warrior temperament, heavy skull. One time he caught a guy sneaking out of a neighbors house. He stopped the guy who picked up a cinder block and broke it over my husbands head. Husband said, “Now you’re going to get it.” The guy ran away, very fast.
I don’t know if I can find any of his DNA. Would his 2 sons have half if I have none, or would it depend on which specific chromosomes they received and the number of genes on each chromosome? Of course, perhaps I have some too. I have very large teeth, and two lateral upper incisors have an indentation which I saw somewhere Neanderthals have. Also I am very strong for my size.
For those who have not read the Clan of the Cave Bear series of books, the author used findings of the Shanidar cave as part of her plot line where a troop of Neanderthals adopt a little hss girl, and live there until the roof collapses killing some.