Former President Trump has arrived at the courthouse for today's proceedings.

This will be the final day of court this week, as court is off on Friday for Trump to attend his son Barron's high school graduation.

Michael Cohen has arrived at the lower Manhattan courthouse for his testimony this morning.

Proceedings are scheduled to get underway at 9:30 a.m. ET.

Testimony is scheduled to conclude at 4 p.m., after which Judge Juan Merchan is scheduled to hear arguments from the parties about the bounds of potential testimony from a defense expert witness.

Michael Cohen returns to the witness stand this morning, where the former Trump attorney is expected to face a full day of cross-examination.

Cohen, under direct examination earlier this week, described in-person meetings and phone calls with Donald Trump, who he said joined into an agreement with tabloid publisher David Pecker to catch and kill negative stories ahead of the 2016 election; approved a $130,000 hush money payment from Cohen to Stormy Daniels; and signed off on an arrangement to reimburse Cohen in 2017 using what prosecutors say were falsified invoices. Trump has denied all wrongdoing.

Defense attorneys are expected to question Cohen's credibility based on his past testimony and previous statements he has made in interviews, podcast and books.

Former President Trump has asked New York's highest court to rescind the limited gag order that prevents him from commenting publicly about witnesses, jurors and lawyers in his ongoing criminal trial, according to a new court filing.

The filing is sealed, but is the next step after an intermediate appeals court yesterday upheld the order imposed by trial Judge Juan Merchan.

Trump has frequently attacked the judge, which is permitted, and has called the limited gag order unconstitutional.

In its ruling yesterday, the intermediate appellate court said that Merchan had appropriately balanced Trump's free speech rights with the court's need to control the trial.

There was no immediate comment from the Manhattan DA's office.

-ABC News' Katherine Faulders contributed to this report

For the second time during the trial, the jury was shown the paperwork for Resolution Consultants LLC, the shell company Michael Cohen formed initially to pay AMI for the Karen McDougal payment.

Cohen conceded he did not give First Republic Bank the "true reason" for the account.

"I'm not sure they would have opened it," Cohen said, if the bank knew the true reason "was to pay off an adult film star for a nondisclosure agreement"

"Need an account opened for Mike Cohen immediately. He wants no address on the checks," Cohen's banker wrote to a colleague on Oct. 13, 2016, when he earlier testified earlier about Cohen's frantic effort to open the two bank accounts in October 2016.

Prosecutors suggested that Cohen misled bankers when he opened the bank account by stating the account was for legitimate business purposes.

Cohen told jurors that he opted to rename the shell company to Essential Consultants after realizing that Resolution Consultants LLC was a real company owned by a friend. The $130,000 payment to Stormy Daniels was made from a new account for Essential Consultants.