Referred the idol by generic name, Naga Deva, as I could not make a positive identification. Maybe this posting will help.
Few distinct features. Both hands are in Abhaya mudra and that reminds me of ‘calm the ocean’ mudra of Buddha. The face does not show any distinct features and it is not worn out. It is probably meant to be that way. He has a long torso and is wearing the sacred thread.
The hood is broken and would have provided an overhead cover. It shows age and lots of it. Tempted to remove the encrustation. In this case, I think it is a job for experts if it ever were to be done.
It is about 7.5 cm in height.
In summary no idea as to who it is, which part of India it is from and how old it is. That makes this a strange blog.
Note: One of the previous owners mentioned this was bought through Sotheby Auctions, probably in the 80s, and it is from Gadag District, Karnataka, India. It was dated to the 12th century.