BTS of Aubrey O'Day's Topless Music Video About Alleged Affair With Donald Trump Jr. Just Posted

Aubrey O'Day is rumored to have written two songs about her alleged affair with Donald Trump Jr., and even made a music vid for one of them, but it was never released.

TMZ posted previously unreleased footage of Aubrey's remake of Gotye's 2011 smash hit "Somebody That I Used to Know" ... in which she's topless with words like "Cheater," "Liar" and "Seduction" written on her body.

The video was shot around early 2012 -- after her alleged affair with DJT Jr. while she was on 'Celebrity Apprentice' -- but was never completed because O'Day failed to pay the production bills.

Aubrey's remix features tweaked lyrics to make it about someone having an affair with a married man ... who seems to fit the profile of Trump's eldest son.

For example -- "You said that was the reason for your pain / But you were scared to ruin your family's name / Your wife's the only one glad we are over."

The song goes on to take shots at the unnamed married man, calling him an "a**hole," "f***ing liar," and "some coward that I used to love."

Aubrey's 2013 tune "DJT" is also allegedly about her affair with Trump Jr. -- whose wife filed divorce papers last week.