Do CISF and various Indian airlines accept ID cards issued to students by their schools (a private school, in this case) as a "valid photo ID" card? The child will be an unaccompanied minor with no other ID document available (they also have an Aadhaar number but not the original card sent by UIDAI at the time of signup. I have read mixed reports about the acceptance of the e-Aadhaar printout).
Air India has this page:
Which says that school ID cards are fine for children. I found similar language in many other airlines' websites (eg: Air Asia - http://www.airasia.com/in/en/about-us/terms-and-conditions-i5.page). Seems like school ID cards are fine in India for domestic travel.