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

Defense attorney Todd Blanche is confronted Michael Cohen with past communications -- with friends and his daughter -- to suggest Cohen was vying to be chief of staff or attorney general after Trump was elected in 2016.

"You told your daughter were disappointed?" Blanche asked about Cohen's response after Reince Priebus was named Trump's chief of staff.

"That I wasn't considered -- yes sir," Cohen said.

Blanche also suggested that Cohen wanted to be attorney general or special counsel the president.

"You told people you would like to be attorney general?" Blanche asked.

"I don't recall that," Cohen said.

An earlier witness -- Stormy Daniels' lawyer Keith Davidson -- testified that Cohen told him that he wanted to be chief of staff or attorney general.

Cohen pushed back on Blanche's suggestion that Cohen wanted a job other than the one he was ultimately given: personal attorney to President Trump.

"I wanted a hybrid position -- one where I would still have the access to President Trump but not be a White House employee," Cohen testified, echoing his testimony from earlier this week.

"You still, even after November, were still looking for a position in the White House?" Blanche said.

"Yes sir," Cohen said before quickly correcting himself. "No."

"I didn't want the General Counsel's office - I made that crystal clear," Cohen said. "There was no shame in being personal attorney to the president of the United States."