A.J. McKee and Patricio Pitbull -- Bellator Featherweight Grand Prix finalists -- do NOT like each other, and it all goes back to ... an autograph?!

"I actually asked [Pitbull] to sign a newspaper," A.J. tells TMZ Sports.

But, instead of just signing the paper ... Pitbull had other ideas, and McKee is PISSED.

"He done crossed my whole face out, picture out. So, I'm f****** him up for that like. Like I lost a lot of respect for him because of that."

And, McKee says he thinks Pitbull's shook.

"I'm in his head so f*****g heavy!"

A.J. and Patricio are the last 2 men standing in a tournament that started with 16 of the best 145-pound fighters in Bellator.

McKee has never lost ... winning all 17 of his Bellator fights -- many of them with ease.

Meanwhile, Pitbull is a legend. He's 32-4 and has wins over Michael Chandler and Juan Archuleta -- to name a few. Patricio is also a double champ ... holding the 145 and 155 lb. titles.

The featherweight title's on the line, but arguably more important is the million-dollar prize!!

We asked McKee what he was gonna do with the cash ... and let's just say this isn't the 1st time he's thought about the 7-figure check being deposited in his bank account.

"Oh, I spent it already bro. It’s spent already. I’m paying off my dad's house. I'm buying a [Porsche] GT 2RS. I need a Porsche in my driveway, man."

FYI, A.J.'s dad is Antonio McKee -- a veteran MMA fighter.

The championship fight goes down Saturday night ... personal beef, a title, and a million dollars are all that's on the line.