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Twelve New Yorkers have been selected to decide Donald J. Trump’s criminal trial in Manhattan, the first for an American president, and alternates are expected to be chosen on Friday should any of the first dozen have to drop out of the trial unexpectedly.

Opening statements, where prosecutors and defense lawyers will introduce their dueling cases to the newly empaneled jury, are expected to begin as early as Monday.

Seven new jurors were added in short order Thursday afternoon, hours after two others who had already been picked were abruptly excused. One alternate juror was also picked before court adjourned for the day, and the selection of alternates was set to resume on Friday morning.

The case stems from a hush-money payment made during the 2016 presidential campaign to a porn star, Stormy Daniels, who at the time was threatening to go public with her story of s sexual encounter with Mr. Trump. The $130,000 payment came from Mr. Trump’s former fixer, Michael D. Cohen, who has said he acted at Mr. Trump’s direction. The Manhattan district attorney, Alvin L. Bragg, charged Mr. Trump with 34 felony counts of falsifying business records, accusing him of having disguised reimbursements of Mr. Cohen to keep the sex scandal under wraps.

Mr. Trump has pleaded not guilty and has consistently denied having had sex with Ms. Daniels. If the jury convicts him, he faces up to four years behind bars.

Here’s what else to know about Day 4 of the trial:

• With a full panel of regular jurors and one alternate already seated, court will commence at 9:30 a.m. Friday. Five more alternates are expected to be chosen. They will vote on Mr. Trump’s guilt or innocence only if a regular member must leave the panel for some reason.

• If there is time in the afternoon, there will be what is known as a Sandoval hearing, which will determine the questions that prosecutors can ask Mr. Trump if he chooses to testify.

• Justice Juan Merchan has ordered news outlets not to report prospective jurors’ answers to two queries on a lengthy questionnaire: “Who is your current employer?” and “Who was your prior employer?” He has also directed that those answers be redacted from the transcript. Read more about the judge’s demands.

• Prosecutors renewed their request that Justice Merchan hold Mr. Trump in contempt of court, arguing that the former president has repeatedly violated a gag order that bars him from attacking witnesses, prosecutors, jurors and others. Justice Merchan said he would take up the matter on Tuesday.