In the 1993 letter George R.R. Martin sent to his agent, the "A Song of Ice and Fire" author explains the original outline for his upcoming fantasy book series. Lots of storylines were entirely different: Jon Snow was in love with Arya (I know, this is crazy), Robb died on the battlefield fighting Joffrey Baratheon, and Catelyn Tully end up killed by the White Walkers in the deep north, not to mention Sansa giving birth to King Joffrey's child. Jaime Lannister's storyline was also really crazy... In the original outline, he doesn't look like the complex, conflicted character we all know and love.
He looks like a beautiful and extremely powerful villain.
Jaime was supposed to be an evil, extremely powerful badass
After Eddard Stark's execution in King's Landing, the war between the Lannisters and the Starks begins. Just like in the show, Robb wins many great victories during the war, but ultimately he is not "able to stand against Jaime and Tyrion" and their allies. After Robb's death on the battlefield, Tyrion besieges and burns Winterfell, forcing Catelyn, Arya, and Bran to flee towards the Wall. Tyrion is also the one who finally removes Joffrey from the throne in disgust of his brutality. Guess who becomes King of the Seven Kingdoms after Joffrey? Jaime Lannister.
King Jaime's reign
Yes, you read that correctly. Jaime was supposed to sit on the Iron Throne according to Martin's original outline for "ASOIAF." And you know how he was supposed to win the throne? "By the simple expedient of killing everyone ahead of him in the line of succession and blaming his brother Tyrion for the murders." King Jaime's behavior was also supposed to lead Tyrion to abandon his family and ride north, where he would have fallen in love with Arya Stark.
What Jaime would have done after is unknown. Considering what George R.R. Martin wrote to his agent, we can only speculate that King Jaime Lannister would have dealt with three major issues: the ongoing war with the Starks, Daenerys' invasion of the Seven Kingdoms (which was supposed to happen in the middle of the story) and - obviously - the White Walkers, "the greatest danger of all." All things considered, we prefer the character Jaime has become in "ASOIAF" and "Game of Thrones" to the one originally imagined by George R.R. Martin. But there's something we must admit: the idea of King Jaime Lannister leading his army into multiple wars, covered in golden armor, it's quite epic.