Here is that marriage - February 1843 (bottom of right hand page)
https://registers.nli.ie/registers/vtls000632289#page/40/mode/1up
Those others names are witnesses rather than fathers’ names but they might be that too. There is an annotation difficult to read but it refers, I think, to consanguinity 3rd degree - relationship.
I agree with heywood. Witnesses (column heading is "Testes"). Consanguinity 3rd degree for both groom and bride. They had a common ancestor (related by blood). Martin and Bridget were the same generation as each other.
Scrawl is hard to read. I couldn't even make out groom's surname.
My original transcription. [ ] = unreadable.
"Martinus [ ]
Brigida Egan
Witnesses Johannes [ ] (same surname as groom), Michaelis Egan
[ ] 3 3
con. [ ]abus
Unsure if date was 26th or 27th. Word in date column is "die" (day) but no number. Previous weddings were 26th. Weddings on next page were 27th. February was a traditional month for weddings.
Reading others with similar notes helps.
2 weddings on same page, 25th Feb.
Michael Egan & Maria Egan con. grad[ ] (Both witnesses Martin Egan)
Ant.. Dorkin & Serah (Sarah) Regan
Facing page:
5th Feb. Jacobus Closs[ ] & Elinora Quin
17th Feb. Patritius Morris & Brigida Ha[ ]
19th Feb. Ro[ ] Regan & Catherina Costello (?)
Comparing all those I think note next to Martin [ ] & Brigid Egan is:
"Im. 3 3
con. gradibus"
"Im" Latin abbreviation for impediment.
P.S. Not relevant to this enquiry but, I saw another interesting note at top of facing page. I think it is about the woman who married that day asking in 1908 for written evidence of her wedding so that she could use it as proof she was old enough (70+) to apply for the new state pension.