UPDATE: On further research…
The original tune is the Blue Bell March by Theodore F. Morse and Edward Mullen composed in 1904.
Kavi Firoz Rustomji Batliwala composed Chaiye Hame Zarthosti.
More on Firoz Batliwala here in an article on his death centenary last year.
It would be interesting to find out which song came first.
Since Firoz Batliwala died in 1912 it would be safe to say that Chaiye Hame Zarthosti preceeded the Nazi Era song that from all pointers came about after WWI.
You can here the tune here. The known tune will start aroun 1:35.
Regular reader Geve Narielwala alerts us to a very interesting factoid.
We leave it to the readers to make their own conclusions.
Below is a clip of Deutschland du Land der Treue, SA
And here is Chaiye