East Belfast loyalist Stephen Matthews has been described in court as acting like a leader of the loyalist group which massed at Pitt Park
Up to 60 masked men allegedly took part in a "display of sinister force" linked to the UVF on February 2.
Stephen Matthews (58), Derek Lammey (56), and David Robert Matthews (34), are jointly charged with unlawful assembly and affray.
Matthews, of Pansy Street, Lammey, from Spring Place and David Matthews, of Millreagh in Dundonald, were arrested during raids on Wednesday morning.
All three appeared remotely at Belfast Magistrates' Court today over their alleged roles.
Prosecution counsel Natalie Pinkerton said the case against them centres on identification evidence.
She told the court neighbourhood police officers saw between 50 and 60 men in the area, apparently organised and there for a common purpose.
At one stage a member of the public pulled up in a "distressed and fearful" state and pointed in the direction of the crowd, the court heard.
It was alleged that Stephen Matthews was spotted near the front of the group "displaying a leadership role".
Even though masks were being worn, the prosecutor contended that all three defendants were identified by build and facial recognition.
She said up to 11 people, including children, were drawn to the nearby Ballymac Centre for safety - remaining there until February 10.
District Judge Fiona Bagnall was told police believe the group of men is linked to the East Belfast UVF.
Opposing bail, Ms Pinkerton argued that the wearing of masks was "highly indicative of those involved clearly knowing this was unlawful activity".
She added: "This involved a display of sinister force."
With none of the three accused charged with any paramilitary offences, defence lawyers challenged the strength of the evidence against them.
Barrister Richard McConkey, for Stephen Matthews, said: "This case has been all over the news, there have been politicians getting involved with complaints about how police dealt with it, and then mysteriously a number of arrests are made."
Michael Chambers, representing David Matthews, argued that the alleged UVF connection should be disregarded.
"The court simply cannot take account of claims in the community that someone may or may not be a member of an organisation," he said.
Bail was refused for all three and Mrs Bagnall remanded them in custody to appear on March 19.