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

"Do you know someone named David Pecker?" prosecutor Susan Hoffinger asked Michael Cohen.

"I knew David Pecker even before Mr. Trump," Cohen replied about the then-National Enquirer publisher. He said the two men would communicate by email or by Signal because "sometimes we thought encryption, not having the event traceable, would be beneficial."

Cohen said he "rarely" interacted with Pecker before 2015. He provided an example of trying to use Pecker to raise for Harlem for Hoops, a charity to which Trump donated.

Before 2015, Cohen testified that the National Enquirer did not purchase stories to kill on Trump's behalf.

He testified he was not aware of National Enquirer parent company AMI ever buying stories for Trump prior to the 2016 campaign -- feeding into prosecutors' narrative this was a campaign-related scheme.

"Prior to Mr. Trump announcing his run for the presidency, are you aware of AMI ever paying to suppress stories?" Hoffinger asked.
"No ma'am," Cohen said.