The Monday raid on Cohen's home and office took Trump by surprise and added to the stress of the Mueller investigation, which is looking into whether Trump committed obstruction of justice and whether his campaign cooperated with Russian Federation to interfere in the 2016 U.S. election.
Wood directed that Cohen be present in court at the next hearing on Monday "so we don't need to have any more adjournments".
But the filing contains the first details released by the Justice Department on the searches, which covered Cohen's residence, hotel room, office, safety deposit boxes and two cell phones.
In addition to Cohen's lawyers, Joanna Hendon, an attorney representing the president appeared and said Trump "has an acute interest in these proceedings".
Cohen is asking for the right to review the documents before investigators do, so he can determine if any information was covered by attorney-client privilege. They said Cohen has told at least one witness that his only client was Trump. People close to Mr. Trump and Mr. Cohen regard the warrant as an attempt by the special counsel, Robert S. Mueller III, to pry into Mr. Trump's personal life - using other prosecutors as his proxy.
"Because the facts underlying this action and the criminal investigation related to Mr. [Michael] Cohen overlap, Mr. Cohen's Fifth Amendment rights may be adversely impacted if this case proceeds", lawyers for Cohen and Trump argued in court regarding Cohen's right against self-incrimination.
Daniels, whose legal name is Stephanie Clifford, has said she was paid US$130,000 by Cohen to keep quiet about a sexual encounter with Trump, and is fighting to lift the terms of the non-disclosure act, which she says was signed by Cohen but not by Trump.
But when the judge demanded that Cohen's lawyers provide some proof that Cohen has any other clients beyond the commander in chief, they twice came back empty-handed.
Once they've reviewed the records, the filter team can give to the investigators communications "between Cohen and persons with whom Cohen undisputedly does not have an attorney-client relationship", likely meaning the records wouldn't be between Cohen and Trump, prosecutors said. Sources who spoke to McClatchy told the publication that "investigators have traced evidence that Cohen entered the Czech Republic through Germany".
In the filing with a court in NY, prosecutors blacked out a section describing what crime they believe Trump attorney Michael Cohen has committed.
Following the hearing Friday, the judge ordered the parties to return to court Monday for another hearing, where Cohen will have to be present.
Prosecutor Thomas McKay, who agreed to do nothing with the seized materials until Monday's hearing, told Wood that Trump should get no special privileges.
Though Wood ultimately granted Cohen's team additional time, she referred to the prosecution's concerns as "well-taken".
On Monday, Cohen's attorney called the searches "completely inappropriate and unnecessary".
"It is common for a civil case to be stayed under these circumstances, and that is what we will be requesting of the US District Court tomorrow", Blakely said in an email.
When your boss is the POTUS, that too Trump, it is hardly surprising that Cohen cared little about the law and order.