Maybe Spinoff Babies
wasn't exactly the trope I was looking for, but it's in the ballpark. Granted, the ones where it's literally supposed to be the same characters, but younger, whether that makes any sense or not, are much more annoying. However, I still find myself wary whenever they do a younger-age equivalent.
When I was younger, I always resented the implication
that for younger people to accept a show, the characters themselves had to be teenage or younger. I still do, of course, but now I'm in the Periphery Demographic
I do hope they mostly stick to, you know, superhero stuff. That's one thing that I think made Teen Titans better, that their age was purely incidental. Their age wasn't important, it was just part of the title. Batman Beyond did okay, all things considered, but it felt the need to ask the question: What if Batman had a bunch of highschool crap to deal with? Answer: I don't care. Actually, the strangest thing I found about Batman Beyond was that Gotham City had apparently gone from a retro, art deco style, to the world of the Jetsons in only 50 years. But that's completely off-topic.
All that being said, I do like the idea of their being a new DCAU series.