There is no Neanderthal Y chromosome (male line) DNA in modern humans, and also no Neanderthal mitochondrial (female line) DNA in modern humans, but about half of Neanderthal DNA is still around scattered between different modern humans. https://www.smithsonianmag.com/smart-news/how-human-y-chromo..., https://theconversation.com/modern-human-dna-contains-bits-f...

Neanderthals and mastodons never met, as they were on different continents.