It turns out the man who was arrested after swimming naked in Kendall Jenner's pool had his sights set on Kylie as well -- showing up at her home after his release from jail -- and it's all laid out in terrifying court docs.

Kendall got a temporary restraining order Thursday against 27-year-old Shaquan King. In legal docs, obtained by TMZ, Jenner states King made it onto her property early Sunday morning, removed his clothes and got into her pool before her personal security ordered him out, detained him and cops came to make an arrest.

What's more frightening, Kendall says a day-and-a-half after his release -- which was only 6 hours because of jail COVID protocols -- King made his way to Kylie's gated community and was arrested Tuesday for felony stalking.

Kendall also details King's alleged criminal history in the docs, claiming he's been busted for kidnapping and has photos of her on his social media pages ... she says he's left her in fear for her own safety.

The restraining order also protects Kylie and Kris Jenner ... and orders that King stay at least 100 yards away.

TMZ broke the story, Kendall has since hired more armed security and left her home, we're told she has no plans to ever return.

We had previously been told King only attempted to get in the pool, but Kendall states in the new court docs that he actually got into the water.