The man, named by the group as Stephen Thorpe, used ropes and climbing gear to scale the side of the Civic Quarter car park yesterday afternoon before being coaxed down by police after a two-hour stand-off.
During the incident the man, dressed in orange, unfurled a banner which read "more rights for dads" and shouted messages to eyewitnesses on the street below.
A spokesman for New Fathers 4 Justice and Stop The War on Dads said: "We were advised this morning of a possible protest in Yorkshire. The protester we are told is Stephen Thorpe
"We have dads from New Fathers 4 Justice and Stop the War on Dads protesting and willing to climb roofs across the country at the moment."
It is understood the protest was in relation to child access issues - and Mr Thorpe is understood to have more protests planned to highlight his cause.
Added the spokesman: "As the courts ignore parental alienation by mothers and refuse to enforce contact orders many dads are left with no other option but to let their children know from rooftops of building that the still love and care about them.
"No parent who is fit and willing should ever be denied their right to share equally in the lives of their own children."
The splinter group is not associated with Fathers4Justice UK which rose to prominence with a number of high-profile protests which saw dads in fancy dress costumes protesting from the rooftops of some of Britain's landmark buildings such as Buckingham Palace and the Houses of Parliament.
The spokesman added: "The present biased, flawed family law system allows children to be exposed to a succession of mums' fleeting boyfriends, lovers and stepfathers with whom they have no biological connection but gives no automatic right of access to their biological fathers or grandparents."