Danny is overworked, over stressed, and he may have just pushed himself a little too hard.
He's been staying up all night, only to go to school, he's always looking over his shoulder for his parents weapons or a ghost attack or a Vlad attack, and there's only so much stress the human body can take before it just tries to force you to slow down.
Unfortunately for Danny, this happens as he's walking the streets of Metropolis while his parents are at a convention.
He starts to see double, can't really tell if he's touching the ground anymore, and runs into a massive chest. He looks up and sees black hair and blue eyes wearing a weird suit.
"Oh, hey dad." Is all he manages to say before he passes out in the man's arms.
Clark panics, but a quick super speed glance around shows that nobody noticed the kid hovering above the side walk before running into Clark's chest with enough force to knock even the Man of Steel back a step before promotly passing out. After calling Clark dad, couldn't forget that.
Clark didn't need to be a world class detective like Bruce to realize this must be another clone situation. One that has freshly escaped from what facility created them and has been surviving on the streets if the numerous injuries Clark could see with his X-ray vision and the ratty clothes the clone was wearing were any hint.
He picked the boy and after another super speed look around flew away faster than anyone could see. He texted Bruce to let him know to hack the cameras and delete the footage just in case, as well as to keep him apprised of the situation lest he panic.
Clark took the boy to an apartment that Bruce maintained as a safe house in Metropolis. He thought about taking him to either the Watchtower or a JL holding facility but he just couldn't do it.
He could admit he had messed up royally with Kon. While he and his first clone had made up and moved past his poor handling of the situation it had forever soured their relationship. He was dedicated to starting this one off on the right foot.
Waking up in a strange apartment would be much better than a cell under red sun lamps. Maybe this way he could actually get to know this clone, this kid. Though he would still have some questions, like why his heart rate was so much slower than it should be.
(It's might not be clear from the text, but Danny ran into Clark Kent, not Superman, so Clark is the one he meets)
The boy slept for almost five hours. He didn't seem to have anything actively threatening his life so Clark just kept an eye on him while he slept. He occasionally had to leave to save someone as Superman, but he did it as quickly as possible so he could return to the safe house.
Bruce had texted him back that the local cameras were scrubbed and that the kid first appeared in a huge crowd of people at the convention center. It would be all to easy for someone with flight and super speed to hide among the people there before making his way into the city.
I can even Clark learn that Danny is trans and just assume that his DNA was not mixed with Lex this time, he doesn't know if he should be relieved, especially since he has no idea who his DNA was with. was mixed this time