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TMZ Sports has obtained an audio recording of the alleged domestic dispute involving Alberto Del Rio and Paige -- in which an emotional Paige screams out, "Stay out of my life. Leave me the f*ck alone."

The person who recorded the audio -- a huge wrestling fan -- says she recognized the couple while they were arguing Sunday in the middle of Orlando International Airport in Florida.

The witness says she recorded the incident as evidence.

You can hear Alberto and Paige yelling -- clearly upset -- with Alberto saying, "Call the cops. Let's do it. Get the cops."

It sounds like he's talking to Paige ... who yells back, "Just stay out of my life. Leave me the f*ck alone. I’m trying to get away from you."

Moments later, Alberto says, "I'm pressing charges against you."

Witnesses tell TMZ Sports it was clear Alberto and Paige were arguing with each other and Paige stormed off at the end of the exchange.

We're told a police officer responded to the scene and spoke with Alberto -- though he was not arrested.

The twist ... Paige issued a statement on Twitter insisting both she and ADR called police on a 3rd party, a female fan, who she claims threw a drink on Alberto when he refused to take a picture with her.

We spoke with law enforcement -- but they made no reference to a 3rd party and told us they were investigating the matter as a domestic violence issue.