That’s funny. Both John and Paul wrote a song called “India” but never published it.
The song written by John Lennon is actually titled “India, India”. It was recorded in 1980 and you can find it in the 2010’s John Lennon Signature Box.
It was originally written for the un-made 1970s play, “The Ballad of John and Yoko” and later used as part of the musical “Lennon”.
The song was inspired by The Beatles stay in India in 1968.

Paul’s “India” can be found in the “secret website” of the Back in the US DVD. It’s just bits from the sound check.