Kanter says he's been under fire from Turkish officials for years for insulting Erdogan publicly -- even calling the guy the "Hitler of our generation."
Other U.S. officials, including Rep. Peter King, have told TMZ Sports ... Kanter's fears are warranted because Erdogan is a bad dude and runs Turkey like a police state.
Kanter has been labeled a terrorist for his comments -- and says officials have even locked his father as retribution.
"If you speak out against Erdoğan, that means you're a terrorist. If he cannot put you in jail, then he will take your family away and put them in jail and say, 'if you don't stop running against me, then I'm gonna keep your family in jail.'"
"That's what he's trying to do, did that to me, that he tried to put my dad in jail, so he thought that I was gonna stop talking, that made me even talk about this more so the world can see it."
As we previously reported, ex-NBA player Hedo Turkoglu -- who's also from Turkey -- ripped Kanter on social media ... saying his claims against the President are baseless and reckless.
Then again, Turkoglu also serves as an advisor to Erdogan.