This is a battery cover for the Original Xbox One Controller. Honestly, I use this battery cover now because it gives my controller some color (not that it looks that cool) but it's also easier to remove than the original one, believe it or not.
I don't have any way of confirming that the new Xbox One Controller is compatible, however, I'd be interested to know if anyone tries it.
This model requires supports and I couldn't really get out of it. I could look into providing a print that already includes supports if anyone is interested.