Other sites have his father as Cathair Mor mac Feideilmid, King of Leinster which fits with the naming tradition that his surname is mac Cathair, meaning son of Cathair. The surname mac Cathair doesn't mean son of Condia.
His father's Wikipedia page lists him among his children:
https://en.wikipedia.org/wiki/Cathair_M%C3%B3r
Fiacha Baicheda mac Cathair Mór, ancestor of Mac Murchada of the Uí Cheinnselaig
https://fabpedigree.com/s056/f537154.htm
lists his father as Cathair Mar Mac Feideilmid aka Cathaeir (Cathaoir) Mor; King of LEINSTER
as does this site:
https://gw.geneanet.org/foullon?lang=en&pz=matheline+marie+herm...
This site:
https://www.libraryireland.com/Pedigrees1/o-toole-1-heremon.php
lists Fiachu as the youngest child of Cathair Mor
His Wiki page:
https://www.wikitree.com/wiki/MacCathair-1
lists his father as Cathair Mór mac Feideilmid
Unfortunately, despite the evidence to the contrary, his father's profile has been isolated as fictional:
King Cathair Mór mac Feideilmid, King of Leinster {Legendary, Book of Leinster}
In any case, the lineage attached is incorrect based on the aforementioned info.
