Obeid, 76, his middle son Moses, 51, and former NSW Labor mining minister Ian Macdonald, 71, are standing trial on charges of conspiring to commit misconduct in public office relating to the 2009 grant of a lucrative coal exploration licence over the Obeid family's farm at Mount Penny in the Bylong Valley in NSW.

They have pleaded not guilty to the charges.

The Twitter account @maardrix, featuring a profile picture of a wolf baring its teeth, was set up when the trial commenced in February and the account’s location is listed as "Supreme Court, Sydney".

The account's background image is a photograph of The Sydney Morning Herald newsroom taken on December 15, 2016, when journalists gathered to watch Eddie Obeid sentenced to a minimum of three years in prison for misconduct in public office over cafe leases at Circular Quay.

Until recently, the account purported to tweet live from inside the courtroom about the evidence in the case and other matters, including the movement of some journalists in and outside the courtroom. It is scathing of the Crown's case and has questioned the credibility of prosecution witnesses, and also takes aim at journalists.

There are about 20 regular attendees at the trial in Supreme Court 9D in Sydney's Law Courts complex, including court staff, legal teams for the prosecution and defence, several journalists and, up until recently, the three accused. Since late August, Eddie Obeid has been appearing remotely.

Journalists have also opted in recent times to observe the proceedings remotely, and there is no jury.

Justice Fullerton said on Wednesday that if any members of the public or parties to the case were "in any doubt" as to whether they were permitted to transmit information about the case from court using a device, they should raise the matter directly with her and she would "consider granting an approval where I am satisfied it is appropriate to do".

Justice Fullerton stressed that it was neither her role nor function, nor her intention, to "police" the use of devices in court, which may be used in court for purposes other than transmitting information about the proceedings.

Justice Fullerton also warned that, if any member of the press or public observing the trial remotely was "misconducting themselves", she would have "no hesitation in rescinding the order allowing them to attend the trial remotely".

A small number of journalists and observers who are identified by name on screen have applied for and been granted court approval to observe the proceedings remotely during the coronavirus pandemic.