The rappers have come to blows on social media after the track - which has been given the unofficial title 'Paranoia' - surfaced online.
The song, which features verses from Thug and Gunna also, didn't end up making it onto the late Brooklyn Drill star's posthumous debut album, 'Shoot For The Stars, Aim For The Moon', which was released last week.
Pusha - who has been at loggerheads with Drake for years - allegedly slams the 'One Dance' hitmaker for paying to have fans throw beer at him on stage and also spits about his arch-nemesis' Toronto gig where a fight erupted.
He raps: ''You know reality bites, it's chess, not checkers/Those empty threats only sound good on your records/ If the patois is not followed by a Blocka/ It's like Marked for Death Screwface, without the choppa/ Let 'em rush the stage when you made like Sinatra/ Only to hide the blade flyin' back through LaGuardia/ I might even buy a home out in Mississauga.''
Thug took to his Instagram Stories to blast his rival and insisted he and Gunna didn't know the verse was about Drake, and if they had, they would have ''made changes'' to the track.
He wrote: ''I don't respect the Pusha T verse on the song with me and Gunna cause I don't have nun to do with y'all beef nor does Gunna, and if I knew that was about him I would've made changes on our behalf...this rapper s*** so gay.''
Pusha has hit back, writing on his own Story: ''Don't feel bad, nobody knew what the verse was abt.
''The label heads that stopped it didn't even know. They only assume because he [presumably Drake] told them! The same way he told abt the Ross 'Maybach 6' verse. (sic)''
He was referring to his verse on an unreleased version of Rick Ross' track 'Maybach Music VI', which was released last year, on which he also allegedly dissed Drake.
Pusha insisted he doesn't need Thug's ''respect'' and demanded Smoke's manager, Steven Victor, removed his version of the song from the deluxe edition of the record.
He added: ''@stevenvictor I demand you take me off the deluxe @realpopsmoke album to avoid any confusion that may take away from This amazing body of work! (sic)''
Drake previously insisted he thinks Pusha has ''made a career'' from their feud.
The 33-year-old rapper became embroiled in a war of words with Pusha after he revealed in a 2018 track that Drake fathered a son he had not yet gone public about, and the Canadian star has argued it remains Pusha's main claim to fame.
He said: ''He's just made an entire career off of it. Some people like his music, I personally don't 'cause I don't believe any of it. And I like to listen to guys I believe.''