There's a lot of very good evidence around that suggests we interbred with neanderthals.
It's generally accepted that
Homo neanderthalensis were either a sub-species of
Homo sapiens or a separate species of the genus
Homo that shared a common ancestor in Africa around 500,000 years ago. The Neanderthals went on to thrive in areas of Europe and the Near East, while Humans lived on the African savannah. As we spread north into Europe, it's believed that we were responsible, along with the effects of climate change, for the eventual demise of the Neanderthals. However, it's well understood that during the period of co-existence, there was some interbreeding between the two species/subspecies.
As a result of many studies, including the mapping of both the Human and Neanderthal genomes, it's estimated that our genetic code contains around 1 - 4% Neanderthal DNA.