Here are a random handful of my favourites with book canon or canon divergence.
Summary: This is how it ends (or Jaime and Brienne and End Game).
Summary: featuring: the quiet isle, chekhov’s wolfpack, someone's bloody wedding, brienne in king's landing, a messy custody battle, dad jaime, a long night that lasts considerably more than a night, and endgame.
Summary: Everything has gone wrong. Brienne delivered Jaime to the Brotherhood Without Banners, but before she could enact the rest of her plan, Ser Ilyn Payne interrupted her and rescued Jaime. Now Brienne is a prisoner, despised by all, with no allies left. Where does she go from here?
Summary: The first time the thought skittered through his mind was as they journeyed down The Red Fork, and he’d quickly dismissed it as a symptom of fatigue, of starvation, an after-effect of spending a year in chains, covered in filth, deprived of company and the warmth of his sister’s body. Cleos was nattering about his horse and Jaime sat propped against a tree, contemplating the woman before him, dissecting the best way to attack and escape, when she pressed her hand into her lower back and pushed inward, her fingers digging into muscles as her spine curved in an arch that had her letting out a quiet groan of relieved pleasure.
Or four times Jaime thinks about Brienne being with child, and the one time he gives it his best shot.
Summary: Stopping for the night at some nameless inn off the Kingsroad, after weeks of pining, Jaime thinks Brienne and he are having a clandestine encounter.
Meanwhile, everyone in earshot regrets endorsing Sansa's plan to force them to share a room.
Summary: “Good and evil… man and woman; ice and fire… black and white, death and life. Life has never been one thing or the other, Lady Brienne. Life is a hopeless smudge of gray. But to the White Walkers—they have no grace for everything that falls in between."
Summary: The realm is on the brink of war, and Jaime Lannister is recently widowed following the death of Elia - his wife and the mother of their young son. Brienne of Tarth has a responsibility she would like to dodge. Jaime doesn't quite understand why she's chosen him as her escape, but he's not going to look a gift horse in the mouth.
Summary: On his way to meet with Cersei at the inn, a recently knighted Jaime sees a girl about to be attacked and intervenes, saving her. He never makes it to the inn, though.
Where one simple decision changes not only Jaime's life but the shape of all Westeros.
Summary: If you want to marry a girl from Tarth, you better gift her a nice sword. Don't bother to come with flowers. Especially with a stupid rose.
Summary: Love is the death of duty.
Summary: Tywin sends Jaime to be fostered at Highgarden under the watchful eye of Olenna Tyrell. After slaying the Mad King, Jaime flees to Essos, and the stories around him grow more fantastic as the years pass. When Olenna summons him to Highgarden for Margaery's wedding to Renly Baratheon, Jaime meets sword-wielding Brienne of Tarth, who might just be his match.
Summary: In which Ned asks the right questions at the right time, and Jaime keeps most of his vows. The important ones at least.
Summary: “Where to now, my lady?” asked Jaime. “You are a lady, are you not? By your speech?” Her jerkin was ripped at one shoulder, but he could see that it had been fine wool.
She shook her head. “I’ve already said too much,” she muttered, staring determinedly at the dirty cobbles.
“Excellent! Away is my destination, too.”
“Why are you following me?”
“Because you don’t want me to.” Jaime grinned. “I like a challenge.”
The Treaty by MotherofFirkins, 29,204 words, Mature
Summary: The Lannisters accept Robb Stark's peace terms, dooming Jaime Lannister to life as a hostage at Winterfell.