More proof Hollywood is a small town ... the first witness at A$AP Rocky's gun trial was an LAPD officer, who just so happens to be the son of Erika Jayne.

Thomas Zizzo was called to the stand Friday as Rocky's trial got underway in a downtown Los Angeles courthouse ... and he told the jury about his ties to the case.

Turns out, Erika's son was one of the cops who responded to the alleged shooting ... and he testified about what he saw at the scene when he arrived.

While Thomas has a famous mother, this is really his first time in the spotlight ... he never appeared on 'RHOB' and Erika doesn't post him on her social media either ... which she says is out of respect for his privacy as a police officer.

Prosecutors say A$AP fired a gun at a former associate, A$AP Relli, back in 2021 outside a hotel in Hollywood ... and the rapper is facing up to 24 years in prison, so there's a lot riding on this trial.

A$AP has maintained his innocence and rejected a plea deal that included about 6 months behind bars ... so he's rolling the dice.

Rihanna's name got brought up a lot in court today too ... and now Erika's got a connection too.

Six degrees of Kevin Bacon!!!