Jury selection began on Monday and could last at least a week.
Trump, the Republican candidate for president in the November 5 election, faces 34 felony counts of falsifying business records to cover up a hush money payment to porn star Stormy Daniels shortly before the 2016 election.
Daniels says she had a sexual encounter with Trump about a decade beforehand.
Trump has pleaded not guilty and denies an encounter took place.
He has called the case, brought by Democratic Manhattan District Attorney Alvin Bragg, a partisan witch hunt meant to interfere with his campaign to unseat President Joe Biden, a Democrat, in the November 5 election.
The three selected included a man originally from Ireland who enjoys doing "anything outdoorsy" and watches both MSNBC and Fox News, a woman who works as an oncology nurse and enjoys taking her dog to the park, and a corporate lawyer who said he does not follow the news that closely.
Earlier on Tuesday, Trump's lawyers and prosecutors began challenging prospective jurors and the judge rebuked Trump for speaking while one potential juror was being questioned.
After lawyers for both sides interviewed 18 prospective jurors who remained of an initial pool of 96, Justice Juan Merchan after a lunch recess called in one potential juror for further questioning about a video she posted on Facebook of people celebrating around the time of the 2020 election.
Once the juror left the room, Merchan said Trump was audibly muttering and gesturing while the prospective juror was speaking.
Prosecutor Joshua Steinglass says the case is not a judgement on Donald Trump's presidency. (AP PHOTO)
The judge told Trump's lawyer Todd Blanche to speak to him about his behaviour.
"I will not have any jurors intimidated in this courtroom," Merchan said.
The judge declined a defence request to dismiss the jury candidate for bias, after she said she could be fair.
The prospective juror said she had filmed the video after going out to move her car and noticing people dancing in the streets and honking their horns, which she said reminded her of public applause for healthcare workers during the COVID-19 pandemic.
In questioning jurors earlier on Tuesday, Manhattan Assistant District Attorney Joshua Steinglass said the case was not a referendum on Trump's presidency.
"This case is really not about whether you like Donald Trump," Steinglass said.
"This case is about the rule of law and whether Donald Trump broke it."
The proceedings so far have underscored the challenges of choosing a jury of 12 residents of heavily Democratic Manhattan who can try the case fairly and impartially.
Roughly half of 96 potential jurors summoned on Monday were dismissed after saying they could not impartially judge the polarising businessman-turned-politician.
Those who remained largely said they could put any opinions they have aside and be fair to both sides.
"I don't think it matters what my political beliefs are, or in relation to the defendant," said one woman, a high school teacher who lives on Manhattan's Upper West Side and enjoys reading and hiking.
Blanche, in his chance to question jurors, said he did not care about jurors' politics but wanted to get a sense of whether they could be fair to Trump as an individual.
"It's extraordinarily important to president Trump that we know that we're going to get a fair shake," Blanche said.
Several prospective jurors said they did not have strong opinions about Trump or said their opinions were not relevant to the case.
"If we were sitting in a bar, I'd be happy to tell you," said one jury candidate, a man who works at a bookstore and enjoys going to Broadway shows.
"But in this room, what I feel about President Trump is not important."
Trump looked toward the panel gathered in the jury box as Blanche questioned them.
