>>149373666 (OP)Batman has to find a vigilante that seems to have set up shop in a different city near Gotham, using all of his trademark tricks and some. As he investigates further, it seems like that person can anticipate every move with uncanny accuracy - not only that, he is making all the decision he would in his place.
Confused and intrigued but also worried that there is something sinister to it he investigates further.
A long mind-game ensues as he tries to catch the person red-handed only to find out it is himself. They meet several times briefly, direct combat rare and fleeting as they both test each other as if instinctively trying to see who is the faker.
The batman this particular series was following was a person who had a split personality brought upon by his mania and worship of the Batman and was later completely overtaken by the facsimile. His broken half, that has now taken a backseat, made deals with powerful enemies of Batman (idk, Joker might like to fuck with bats this way) to fund him so to us it does look like he is the real deal and to him this was the final nudge into the abyss.
Batman has a double convinced that he is the real deal and so it the reader until the very end, where their fight is interrupted by some form of danger that makes both bats spring to save them and the faker manages to get the upper hand, temporarily disabling batman so that he alone can sacrifice himself to save a bunch of civvies.
I haven't fleshed it out beyond this and maybe this was already done before (you kinda never know until you dive deep) , but if not, hey free idea.