Dia dhuibh!

I am sorry to specify at once that I just made a mistake sending this letter attached to one of your topics I was reading, i;e; Lirici. Sorry for that!
Well, let me start again ! and let me introduce myself : my name is Jean . I am a Frenchman and I am trying to re-learn Irish, a beautiful language which means so much to me . I used to speak a little Irish when I was a little boy since my mother was Irish and one thing I cannot remember is the correct spelling of the family name "HALLIGON" , in Gaeilge. I remember seeing a little "h" and a big "A" on some of my mother's papers (or maybe grandmother's)(and that sounded odd) and that was certainly because of a spelling like this one :"Ni hAilleagan" (excuse me for the lack of fadas!). But Was it" Ailleagain ", "Ailleagoin "or... anything else . Could one help me find it?
Thanks a lot!!!
Go raibh maith agaibh! Jean

Dia's Muire duit,
This is from "Irish Names and Surnames" by Rev. Patrick Woulfe (p. 549):
"Ó hAilleagáin...Halligan..also Ó hAllagáin; an old Ulster surname; now common also in Mayo and Roscommon"

In "The Surnames of Ireland" MacLysaght states:
(O) Halligan Ó hAileagáin. An Oriel sept of Louth and Armagh. He also says (O) Hallahan, Hallighan Ó hAileacháin. A Cork and Waterford family often confused with Halligan.
The feminine would be Ní Ail(l)eagáin