The actress was spotted filming her new show, "The Better Sister," Tuesday in NYC ... where she appeared unfazed by her hubby's recent legal drama in Sag Harbor, which is a couple hours east of where she's shooting in the Big Apple.

Jessica stunned in her costume for the Prime Video series ... wearing a body-hugging black and tan dress while sporting a chic bob. The actress -- who has been married to the *NSYNC alum since 2012 -- smiled wide while waiting for her moment in front of the camera.

She was later photographed with a serious expression on her face, but she could've just been focusing on a scene ... it's a crime thriller, after all.

Though, we wouldn't blame JB if she had other things on her mind.

As we previously reported ... JT was pulled over in Sag Harbor Monday night after blowing through a stop sign and swerving on the road.

According to our sources ... Justin was enjoying a night out with friends at the American Hotel before getting behind the wheel of his gray BMW UT.

He was stopped by police a little over a mile from the hotel ... where officers performed a field sobriety test on him.

While JT refused to take a breathalyzer test, cops say the singer had bloodshot/glassy eyes, a strong odor of alcohol on his breath, and slowed speech at the time. They slapped cuffs on Justin and took him to jail ... where he spent the night.

He was arraigned and released without bail Tuesday morning ... looking downcast as he exited the courthouse with his attorney.

So far, Jessica and Justin have remained tight-lipped about his arrest ... though he's expected in court on July 26.