Your gateway to endless inspiration
Tim went mad scientist during the search for Batman and he cloned himself just in case he died. The objective was to retain all knowledge even if the original was dead, so he wore a chip that would feed knowledge to the clone that was in stasis.
All of this was a contingency for Ra's interest and the LOA's meddling. However, it so happened that Phantom was launched across universes and he landed by complete coincidence inside the gestating clone. The overshadowing was so shocking that it put Phantom to sleep for a couple of weeks. When he woke up, the pod sprang open and Danny fell down to the ground face first. Turns out Tim's heart flatlined for a couple of seconds while he was trapped with the LOA, and that was enough for the clone to be released and the chip connection to be cut.
Now Danny, naked and completely bewildered, is having contrasting information in his head about himself. He's Danny Fenton, half-ghost screw up, and he is at the same time Tim Drake, genius superhero that just died at the hands of Ra's. He has to investigate how to go back to his own world and he has to look into Bruce's disappearance to bring him back.
The whole thing is a literal headache, and Danny settles for using the gadgets and clothes Tim had left for him.
Having the brain/memories of a genius comes as a gift. However, Danny still doesn't realize that he's overshadowing someone and goes out to do some recon of his own.
He wants to see if there's really a Batcave in Wayne's basement.
Amnesiac Danny is wondering around the streets of Gotham and when Bruce comes across him, he thinks it's Jason; first as a hallucination and then after he manages to touch him, as some trick someone was trying to pull on him. Except… Danny even has the right clothes on! All muddy and dirty… Alas, when they check Jason's grave, there isn't anyone inside, leaving them with the wrong conclusion that Danny/Jason must have broken out of his grave.
DNA analysis is inconclusive. Every sample comes back as corrupted. Danny and Jason DO look the same and the similarities are convincingly enough to fool Alfred as well. Dick wasn't around too much, so at this point he also thinks Danny could be Jason.
Could, but the situation is… odd. Everyone is left standing wrong-footed. This Jason has no answers and all they have are a bunch of… hypothesis that they cannot test.
Even so, Bruce cannot help himself and tries to make Danny "remember". Eventually this leads to Danny thinking of himself as Jason, pointedly not thinking about how some things don't add up after he starts living in Wayne Manor.
And then enters Tim Drake, whose first act after being introduced is to say that Danny is a fake.