Fianna Fail TDs have raised serious concerns about the Ceann Comhairle's office and the amount of speaking time they have been allotted since his appointment.
The TDs have raised the matter with the Houses of the Oireachtas and also internally within Fianna Fail, claiming they are not being given the same access to Dail debates as their colleagues.
The current Ceann Comhairle, Sean O Fearghail, is a Fianna Fail TD for Kildare South. The three TDs who have raised concerns are his constituency colleague Fiona O'Loughlin, Kildare North- based TD James Lawless and Meath East's Thomas Byrne.
It is understood the dispute was sparked by comments made during a heated debate in the Dail bar between Fianna Fail political staff.
The comments were reported back to the TDs who raised the matter internally within the party.
The row has resulted in at least one confrontation in Leinster House between the Fianna Fail TDs and a member of Mr O Fearghail's constituency staff.
Mr Byrne, who is the party's education spokesman, wrote directly to the clerk of the Dail, Peter Finnegan, about what he felt was unfair treatment from the Ceann Comhairle's office.
Central to Mr Byrne's complaint was a claim that he was not chosen to speak on the teacher strikes during the topical issues segment of the daily debates - despite submitting requests several times over the course of two weeks.
Mr Byrne also raised the matter with Fianna Fail leader Micheal Martin's advisers, who told him they were not going to get involved in the dispute.
Ms O'Loughlin wanted to highlight issues facing older people in Kildare, and Mr Lawless was also concerned he was not being given access to topical debates. All three of the TDs discussed the matter privately among themselves.
TDs must give the Ceann Comhairle's office notice in writing of what issues they would like to raise with ministers under topical issues.
The Ceann Comhairle then selects four of these issues for each sitting day.
Those selected can make a statement and question ministers on any issue relating to their department.
A spokeswoman for the Ceann Comhairle's office insisted that Mr O Fearghail was careful to ensure that all TDs were afforded an equal amount of speaking time in the Dail.
"The Ceann Comhairle would be very rigorous in making sure that everybody gets their turn in the criteria that is set down for topical issues," she said.
"It would be fairly done and everyone gets their turn once they meet the criteria."
A senior Oireachtas source insisted that Mr O Fearghail was "one of the fairest" Ceann Comhairles to hold the office. "He hasn't put a foot wrong," the source insisted.
All three of the TDs have had an opportunity to speak during topical issues since the matter was raised.
None of the deputies wished to speak about their concerns when contacted by the Sunday Independent.
Mr O Fearghail is the first TD to be elected as Ceann Comhairle through a secret ballot.
He saw off competition from Fine Gael's Andrew Doyle and Bernard Durkan, Sinn Fein's Caoimhghin O Caolain and Independent Maureen O'Sullivan.
He replaced Fine Gael's Dun Laoghaire Rathdown TD Sean Barrett.
Since taking office Mr O Fearghail has proven to be popular among staff in the Ceann Comhairle's office and is seen as an even-handed chair of the Oireachtas Business Committee.
Before his appointment he served as Fianna Fail's chief whip and was also a member of the Committee on Procedure and Privileges.
The Ceann Comhairle's office is one of the most coveted positions in Leinster House as the holder is automatically returned to the Dail at the next election.