A$AP Rocky might have a beloved baby mama, but it looks like that ain't going to help him in this trial ... 'cause prosecutors are weeding out prospective jurors with Rihanna questions!

Jury selection is currently proceeding in A$AP's trial after he turned down a plea deal and decided to fight the gun charges he's facing ... and, potential jurors are getting asked a ton of questions about both A$AP and his better half.

Among the questions they're being asked ... whether they've heard of A$AP or Rihanna, listened to their music, or downloaded any of their songs.

They're also asking people if they've bought any of Rihanna's products -- like the clothing or makeup released under her Fenty label. So, if a juror wanted to look like RiRi in her viral yellow lace underwear or her new Les Roses collection, they might be getting the axe from jury duty soon.

The prosecution also asked the jury pool if they could render a fair and impartial verdict if Rihanna happened to be sitting in the courtroom.

As you know ... A$AP's been in court all week while readying for his trial to commence -- and, while not much has happened yet, Rocky's lawyer, Joe Tacopina, told us Wednesday that jury selection's ongoing.

ICYMI ... Rocky was offered a deal by prosecutors -- promising if he pled guilty to one felony charge, then he'd serve 180 days in jail and three years' probation. Rocky turned down the deal and -- if convicted -- he could face up to 24 years in prison.

Prosecutors claim video shows Rocky holding a gun while in a physical altercation with A$AP Meli -- his former friend who accused him of assault. Tacopina claims the gun was a prop used for show.