About the AU
In this AU, dragons used to live alongside humans and monsters. They were seen as mere wild animals by the humans, but as friends by most monsters. All in all, they still coexisted peacefully.
When the war broke out, dragons decided to side with the monsters, as the two races have helped each other out countless times. Even though they still lost the battle, a few humans had been killed by dragons, but their souls were never collected. When the monsters were defeated, every single dragon was exiled to the Underground as well. Their population had decreased to a worrying extent, and most species disappeared after the massacre.
Grateful for their help, Asgore declared a new rule: that dragons would be treated with respect, and could be kept as pets and close friends if the creatures accepted. Ever since then, both species worked together. Almost every monster in the Underground owns a dragon, even though there are wild ones as well. Both races live in peace.
Dragons are aggressive to any human; however, more than a few of them are curious, and have even befriended the fallen humans before they were ultimately killed. They can sense the humans' intentions, and will grow extremely aggressive if they see a human with murderous intent. As for one that helps the monsters, they will be confused.
All of the main characters except for Napstablook, Flowey, Mettaton and Frisk (initially) own or owned a dragon:
Morning: Morning is Toriel's dragon, a Terrible Terror. They love each other dearly, and Toriel treats her like a cat. Morning is often mischievous, but is sweet and playful, and seems to be one of the few dragons who are comfortable around humans. She is the one to save Frisk from Flowey and guide them to Toriel; she follows them around until they leave.
Bones: Bones is Sans' dragon, a lazy, grouchy and selfless young Boneknapper. He is not a fan of flying and is often seen sleeping along with Sans. Papyrus' dragon, Rattle, treats Bones like a younger brother. The trait that differs him from Rattle are his purple eyes. Frisk meets Bones before they meet Sans, as the dragon was trying to scare them. His own firepower replaces Sans' Gaster Blasters, and he flies away if his owner is killed.
Rattle: Rattle is a young Boneknapper, and Papyrus' dragon. He is fussy and loud, always trotting around Papyrus like a dog and constantly asking for attention. He knocks things over more often than not, but is really careful around his owner's puzzles and even tries to help sometimes. He is very fond of Frisk. The trait that differs him from Bones are his red eyes. He flies away if Papyrus is killed, not before giving the human a long glare of disbelief.
Exterminator: Undyne's dragon, a proud and fierce Razorwhip. She and Undyne get along swimmingly, and are always together on the look for humans. She considers Papyrus and his dragon Rattle to be her best friends, and acts like an angel around them, but is really aggressive around Frisk until things settle down - she then acts like a grouchy cat around them. If Undyne dies, Exterminator will keep fighting until the end.
Goggles: a lazy Gronckle, and Alphys' pet dragon. He loves to eat paper, and Alphys usually finds herself trying to snatch her paperwork from his jaws. Overall, Goggles is almost always found sleeping and doesn't fly much, since his owner is afraid of riding a dragon. Mettaton is not very fond of him as he often trashes his shows. If something happens to Alphys, he's never seen again.
Stormcutter: Stormcutter is a... Stormcutter, and Asgore's dragon. He is a proud and elegant creature, always respectful and loyal toward the king. He acts friendly around anyone, even around Frisk until the time of the battle comes - even then, seeing that the human has no dragon to help them fight, holds back a lot. He accepts whatever choice Asgore makes. Toriel is gentle around him.
Teddy: Teddy is Asriel's dragon, a Night Fury. She and Asriel got along like siblings, and was always glad to spend time with Chara and their dragon, Rain. Teddy is frolicsome and loves to fly around. She never left Asriel's side, but when he, Chara and Rain died, she never flought again and stayed by Asgore's and Stormcutter's side. On a Pacifist ending, ecstatic to see her friend again, she joins Asriel in battle but refuses to use her true strenght. Asriel decides to let Frisk keep her in the end, worried he might hurt her.
Rain: Chara's dragon, an elegant and mischievous Death Song. They found her while they played with Asriel and his dragon, alone and afraid. Rain, curious around humans, soon befriended them, and they became a close pair who understood each other. Refusing to leave them after death, she followed Asriel to the surface and attempted to protect him, but was captured and killed by the humans. On a Genocide route, she will appear alongside Chara, equally sick and twisted.
Others: Grillby owns several Fireworms, Nice Cream Guy is often seen with a Terrible Terror that follows him around, Gerson owns a Scauldron, Burgerpants has a Hotburple, and Catty and Bratty own two Deadly Nadders.