Denisovan DNA has been found among a large number of First Peoples of both North and South America. How they received such ancestry is still open to debate, but whatever the case it does tell us that Denisovan hybrids probably did thrive on the continent.
I bring out all this in my contribution to Greg Little's book Path of Souls: The Native American Death Journey, published in 2014. Here is the link to an online version:
It is contained also in a new book I have done with Dr. Gregory Little to be published next year called Denisovan Dawn: Hybrid Origins, Gobekli Tepe, and the American Genesis. Here is Greg's blog on the subject, published this week:
As to India, the Denisovans are most likely remembered as the Asuras, the demons, in particular their association with the story of the Churning of the Milky Ocean.