There might be fan art, but I doubt there’s anything official. Besides how little attention anything Elsweyr generally gets (even the first ESO expansion into Elsweyr mostly had the khajiit as secondary characters), it originated in an unofficial source. Michael Kirkbride (a lead writer for Morrowind and several other important bits of Elder Scrolls stuff) wrote The Pocket Guide to the Empire, 2nd Edition with the input of community members. The Pocket Guide 1st edition came with the manual of Redguard, and the 3rd edition came with Oblivion. The 3rd edition contains a few references to the 2nd edition, which at the time had not actually been written, so Kirkbride decided to fill the gap. The relevant section, with explanatory notes from me that you can ignore if you know that stuff already, is:

So Mane ^1 saw that Khajiit was fighting itself more than usual and donned the hairs of his many littermates and his clan and his guards until he could bear no more and then palanquin-raced throughout the lands to repeat these words: “Woah-ho now, mad cat. You fight and fight but if you will give Mane just one moment, he will show something far better, for the Mane has had many hours and fine sugar to think this over. Come now, Palatiit ^2 ; come now, Ne Quiniit ^3 . Together, just this once, Khajiit will stand tall as Alkosh ^4 , cat upon cat upon cat. And in doing so, it will climb to the moon as it has been told so many times.”

Khajiit saw reason in these words and so it climbed and climbed, cat upon cat, for a hundred days. Much sugar ^5 was brought there to support the climbers and in the end Khajiit climbed high, so very high that it was in fact closer to Jo’Segunda ^6 than to Nirni ^7 below. At that moment, little Alfiq ^8 fell upwards and from there on Khajiit helped Khajiit up, which was down, until all were gathered there. This is where Khajiit intends to stay from now on, for who could know strife when walking sugar and not sand?

1 - The Mane is the religious leader of the khajiit 2 - Pa’alatiin, or Pellitine, is the southern half of Elsweyr. Elsweyr is the region that the khajiit are from, and had only recently been united when the 2nd edition was written in-universe 3 - Ne Quin’al or Anequine is the northern half of Elsweyr 4 - Alkosh is the khajiiti interpretation or version of the god of time and top god of most pantheons, generally known as Akatosh to the empire and therefore in most game material 5 - Moon sugar is a narcotic with great religious significance in khajiiti society. If you’ve come across skooma in the games, it is the heroin to moon sugar’s opium 6 - Jo’Segunda, or Secunda, is one of the two moons 7 - Nirni, or Nirn, is the planet that Tamriel and the games are set on 8 - An alfiq is a type of khajiit that physically resembles a housecat but which is every bit as sapient as any other khajiit. You can actually meet several in ESO, but sadly cannot play as one. The Legends card “Frazzled Alfiq” is probably my all time favourite piece of official Elder Scrolls art

Anyway Kirkbride’s unofficial stuff is not “canon”, for whatever that’s worth, but due to his significance to the setting and the fact that his writing is usually interesting, people often accept it as such. The story does not end there, though! The developers of ESO have a series called Loremaster’s Archive, which is an in-character lore Q&A series. In “Moon Bishop Hunal Answers Your Questions”, someone asked about the “cat upon cat” story.

“Our scribes are currently working on the transcription of the ‘Ri’datta-ssabavezi.’ In this story, your people are climbing ‘cat upon cat’ and finally reach Jone, where they founded something called ‘Lleswer.’ But we failed to understand the meaning of this. Some at the Guild suggest it has to be taken literally, but it seems impossible. Am I right?” – Iszara the Restless, Singer of the Scenarist Guild

Moon Bishop Hunal says, “It is the nature of myth to be true and yet at the same time mere allegory. Are you ‘right’? In this context, the question is without meaning. But do not be offended, hairless one. Many stories are puzzles with more than one solution.”

So, canon? Maybe, maybe not. But it got a nod, and people like it.