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Jake Paul claims Tommy Fury turned down a TON of money to meet him in the boxing ring again ... but TNT insists that's not the full story.

Paul sounded off on social media Tuesday morning ... saying while plenty of fighters agreed to step in for Gervonta Davis , one person in particular didn't.

"Guess who didn't say yes even for $15M. Bitch made you and your father are, who controls everything you do. You are not a man. You are a boy. Daddy's little boy."

While people wondered who that could be ... Fury put an end to that speculation -- calling Jake out for offering him a fight in America, "a place I can't get to right now."

"Offer me the same $15M anywhere else in the world and I'll be there in 8 weeks to shut you the f*** up and repeat what I did the first

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