I'm going by a weird mixture of TS!Underswap and Classic Underswap. So some things may not be how you expect them to be. Explanations for that will be at the bottom... if I feel like it.
Also I was too lazy to do Error's glitchy speak- I'll go back and fix it later.
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Quill's story...
"Hey, guys. Lemme tell you my story. Stretch and Blue have shared theirs, and Error doesn't remember most of his, so it's only fair that I share my own now."

"I was born in a Swap AU, Inkswap to be precise. I was around 6 years old when my little brother was born, and barely a year later, our father disappeared. I don't think my little bro remembered Gaster, he wasn't even a year old after all. Our father sent a letter to me somehow, saying that he had ended up in the Void and that he'd find his way out eventually."

"My bro and I lived with the Royal Scientist, Dr. Rivers, until they (Dr. Rivers) fell into the Core when I was 14. I tried to save them, but nearly fell in myself. The backlash from the disruption of the space-time continuum hit me, and it had a permanent effect on my magic, right on down to my core. My magic is a lot more disconnected from reality than most, just like the majority of Judges from Original AUs. That disconnect left me with the ability to shortcut, and remember resets."

"I finally heard from dad again a few weeks later. Apparently he had gotten stuck in the void with a bunch of alternate versions of himself. One of them had finally managed to make a cross-dimensional phone, so he could contact us. He told us that he wished he could've seen us grow up, he loved us, and he also told us about his house in Snowdin, where we could live."

"After that, tibia honest, my story was very similar to yours for a while, Stretch, or at least what I can remember of it. It's really fuzzy during this point, and I feel like some of it is missing entirely, but... well, it's not like I can do anything about it."

"My little bro had always been the most important thing to me, and when he wanted to join the Royal Guard, I suggested he talk to Alphys, and I went and got several sentry jobs of my own. My main post was in Snowdin, but I also had posts in Hotland and Waterfall."

"A few years later, the RESETs began. The first time the kid arrived, I was terrified. I was scared for my bro, as even if the kid hurt him, I had promised Asgore to protect them. I was scared that everything I'd worked so hard for would fall apart. The kid didn't hurt him, though. And for that, I was grateful."

"Then, later that day, a few hours after I took the kid out for a snack at Muffet's to express my gratitude... something in the magic of the world shifted. I found myself back at my Waterfall post, when I had just been at my Hotland one."

"Then it happened again, and again. Temmie paid me a visit at one point and well... angry doesn't describe how irritated she was. She ranted about time and space, and her power being stolen from her. She returned again after the next shift, and began complaining about "that stupid Determined kid." I asked her if she knew why the timeline kept jumping back, and she told me how the RESETs worked. I owed her a debt for that."

"As you can probably tell, our Temmie was a lot nicer than most of them are, or at least to me. That doesn't mean that she wasn't a jerk to most people though, heh. She called in that debt when our world was falling to pieces, and I don't break my promises, so she's somewhere in Startale now, probably keeping that nutcase of a talking star lily company."

"Time eventually stopped jumping back after the kid finally made it past Alphys. They almost killed her, actually, although not on purpose. She had chased them into Coldsea, and as a a reptilian monster, the cold and wet there really didn't agree with her."

"You probably know the story of the resets and such after that... we had some pacifist, some genocide, but the kid was mostly pretty neutral, and would only fight if they felt cornered and had no other opinion."

"After I don't even know how many resets, something changed. Our world began to fall to pieces, and my brother was the first to disappear. As you would expect, I was scared and really worried- who know where he went? Even now, I still don't know if he's even alive... I'm still holding onto my hopes of him being okay, though. He's a tough lil monster, and he wouldn't give up easily. He was the sweetest dude imaginable... I miss him so much," said Quill, inky tears dripping down his face.

"I'm sure he's out there somewhere, Quill," said Error. "I don't think I've met him, but he could be in the Omega timeline, which I can't enter, or he could be somewhere in the Void with the Gasters. He could also be in an AU like Songtale- it doesn't reset or experience many timeline shifts, and it's a hub AU... Heh, I could've met him when I went there and never even realized that he didn't belong."

"No... he wouldn't stay in one place. Even if he lost his memory or something, he'd know that something was missing deep down in his soul, and he'd go searching for it. Our portals can hop short (like one AU over) inter-dimensional distances, so he really could be anywhere."

"Welp. Maybe someday we'll find him. If I do, I promise I'll bring him back to you... and I don't take promises lightly," said Error.

The story continues in Startale's origin story, "Supernova" and "An Error In The Stars- Shifts In Space Time."