There are several chess variants like that. The original "battle chess variant", of course, is Edgar Rice Burroughs' Jetan.
Chesslike
I have yet to see a variant like mine, even Jetan doesn't appear at all similar, but perhaps I didn't find the variant you are referring to when searching. I would have loved to call it Battle Chess, because that's what it is... but sadly that title is seen as something that my game is not.
My comment was not meant to downplay your variant, or to suggest that it was unoriginal. Sorry if I chose bad wording. I just wanted to point out that there is an entire genre where your game fits in. Some may be similar to yours, but since I do not know any details, I really cannot say. The title Battle Chess is already in use by a classic computer game, so may be confusing if you were to use it. Combat Chess has been used as a generic name for this kind of chess, but as far as I know, the title is not taken, so might perhaps be used for your variant if you like.
Ever wondered what it would be like to play chess where all the pieces had hit points and other battle stats? Instead of instant capture, you have to battle it out to remove the piece from the board, but be careful because you could lose your piece! Classic chess strategies don't apply and some moves don't exist, in order to win you have to remove the opponents King from the board through battle.
Chesslike is exactly that! Available on Steam now