If we make an identical copy of you, then both copies think they are the original conscious identity; and in all important senses, they are both right.
Only an external observer can make the claim that A or B is 'the' original; and that observation is flawed - neither person is the physical individual he was yesterday.
As I have said before, you don't even have continuity of conscious identity with your 'yesterday self'; I suspect that the reason you have fallen into a cognitive trap here is that you observe apparent continuity of identity associated with continuity of (the vast majority of) physical structure. People typically persist in a mostly unchanged state from day to day, rather than being assembled atom by atom by highly advanced aliens. But whichever happened to get to where you are now, the result is indestinguishable.
Make an exact copy, and the two individuals are BOTH correct to claim to be the real 'I'.
By making a copy you end up with two brains, two hearts, and two consciousnesses.
It really is that simple. You are making it needlessly complex, probably because you are hung up on the illusion that identity is tied to the current physical body you inhabit. It is not - it is an inseparable property of your brain. Dualism is beguiling, but it is bullshit - even when it is sneaking in under your radar and you don't even realise you are doing it.