No. Or, at least, not so far as we can tell. IIRC, the easternmost extent of the known range of Neanderthals is around Iran or maybe the northwestern extreme of Afghanistan. Not a long way from India, but nevertheless not quite that far. read more
Neanderthals never inhabited India and no fossil remains of any kind traced till now. The only fossil remains of India are that of Ramapithecus from Siwalik hills and Narmada man (Pithecanthropine (Homo erectus) from the Narmada valley. read more