Prosecutors in the New York hush money case against Donald Trump have asked a judge to fine the former president 3,000 dollars over social media posts about key witnesses.

The request was made on Monday ahead of jury selection, with prosecutors from the Manhattan District Attorney’s office seeking a 1,000 dollars fine for each of three posts they say violate gag order that bars him from commenting on witnesses.

Last week, Trump used his Truth Social platform to call two important witnesses – his former lawyer Michael Cohen and the adult film actor Stormy Daniels – writing they were “two sleaze bags who have, with their lies and misrepresentations, cost our Country dearly”.

Trump had earlier arrived at the New York court for the start of jury selection in his hush money trial, marking a singular moment in US history.

It is the first criminal trial of a former US leader and the first of Trump’s four indictments to go to trial.

Because Trump is the presumptive Republican presidential nominee, the trial in Manhattan will also produce the split-screen effect of a candidate for the White House spending his days in court and, he has said, “campaigning during the night”.

At the outset of Monday’s court proceedings, Judge Juan M Merchan denied a defence request to recuse himself from the case.

Additional legal arguments and housekeeping matters were expected before the formal start of jury selection.

To some extent, it is a trial of the US justice system itself as it grapples with a defendant who has used his enormous prominence to assail the judge, his daughter, the district attorney, some witnesses as well as the allegations against him – all while blasting the legitimacy of a legal structure that he insists has been appropriated by his political opponents.

Against that backdrop, scores of ordinary citizens are due to be called on Monday into a cavernous room in a utilitarian court to determine whether they can serve, fairly and impartially, on the jury.

Judge Merchan wrote in an April 8 filing: “The ultimate issue is whether the prospective jurors can assure us that they will set aside any personal feelings or biases and render a decision that is based on the evidence and the law.”

Trump has pleaded not guilty to 34 felony counts of falsifying business records as part of an alleged effort to keep salacious – and, he says, bogus – stories about his sex life from emerging during his 2016 campaign.

The charges centre on 130,000 US dollars (about £104,000) in payments that Trump’s company made to his then-lawyer, Michael Cohen.

He paid that sum on Trump’s behalf to keep porn actor Stormy Daniels from going public, a month before the election, with her claims of a sexual encounter with the married mogul a decade earlier.

Prosecutors say the payments to Mr Cohen were falsely logged as legal fees in order to cloak their actual purpose.

Trump’s lawyers say the disbursements were legal expenses, not a cover-up.

The former president himself casts the case, and his other indictments elsewhere, as a broad “weaponisation of law enforcement” by Democratic prosecutors and officials. He maintains they are orchestrating sham charges in the hopes of impeding his presidential run.

After decades of fielding and initiating lawsuits, the businessman-turned-politician now faces a trial that could result in up to four years in prison if he is convicted, though a non-custodial sentence is also possible.

Regardless of the eventual outcome, the trial of an ex-president and current candidate is a moment of extraordinary gravity for the American political system, as well as for Trump himself.

Such a scenario would have once seemed unthinkable to many Americans, even for a president whose tenure left a trail of shattered norms, including twice being impeached and acquitted by the US senate.

The scene inside the courtroom may be greeted with a spectacle outside. When Trump was arraigned last year, police broke up small skirmishes between his supporters and protesters near the courthouse in a tiny park, where a local Republican group has planned a pro-Trump rally on Monday.

Trump’s lawyers lost a bid to get the hush money case dismissed and have since repeatedly sought to delay it, prompting a flurry of last-minute appeals court hearings last week.

Among other things, Trump’s lawyers maintain that the jury pool in overwhelmingly Democratic Manhattan has been tainted by negative publicity about Trump and that the case should be moved elsewhere.

An appeals judge turned down an emergency request to delay the trial while the change-of-venue request goes to a group of appellate judges, who are set to consider it in the coming weeks.

Manhattan prosecutors have countered that a lot of the publicity stems from Trump’s own comments and that questioning will tease out whether prospective jurors can put aside any preconceptions they may have.

There is no reason, prosecutors said, to think that 12 fair and impartial people cannot be found amid Manhattan’s roughly 1.4 million adult residents.

The process of choosing those 12, plus six alternates, will begin with scores of people filing into Judge Merchan’s courtroom. They will be known only by number, as he has ordered their names to be kept secret from everyone except prosecutors, Trump and their legal teams.

After hearing some basics about the case and jury service, the prospective jurors will be asked to raise hands if they believe they cannot serve or be fair and impartial. Those who do so will be excused, according to Judge Merchan’s filing last week.

The rest will be eligible for questioning. The 42 preapproved, sometimes multi-pronged queries include background basics but also reflect the uniqueness of the case.

“Do you have any strong opinions or firmly held beliefs about former president Donald Trump, or the fact that he is a current candidate for president, that would interfere with your ability to be a fair and impartial juror?” asks one question.

Others ask about attendance at Trump or anti-Trump rallies, opinions on how he is being treated in the case, news sources and more – including any “political, moral, intellectual, or religious beliefs or opinions” that might “slant” a prospective juror’s approach to the case.