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

Jurors saw the form that Michael Cohen used to create the account for Essential Consultants LLC, the shell company he used to pay Stormy Daniels the $130,000 per their nondisclosure agreement.

"MICHAEL COHEN IS OPENING ESSENTIAL CONSULTANTS LLC AS A REAL ESTATE CONSULTING COMPANY TO COLLECT FEES FOR INVESTMENT CONSULTING WORK HE DOES FOR REAL ESTATE DEALS," the form said.

Asked about the veracity of the form, Cohen responded, "It's false."

Cohen said he filled out the form that way "to hide the intent ... which is to pay for a nondisclosure agreement."

Cohen said had he been honest on the form, the account would not have been opened by First Republic Bank.

Prosecutor Susan Hoffinger then walked Cohen through each of the documents used to create the shell company then wire $130,000 to an attorney-trust account for Stormy Daniels.

Cohen stated that wire transfer form he used for the payment was not truthful because it stated the purpose of the wire was a "retainer."

In reality, Cohen said, the wire was "in order to pay Stormy Daniels to execute the nondisclosure agreement and to attain the story -- her life rights."