You may already know this, but I found the following...
Alexander Hamilton Phair born 12 dec 1885 was baptised in Ballinamallard methodist Church.The entry shows his father's name & mother's first name.Four of his siblings were also baptised here.The family are in the 1901 census, his mother and six children, his father is dead.By the 1911 census only two children are still at home.
Children of William Phair(or Fair) & Catherine Jane ?? baptised in Ballinamallard Methodist Church.
Edwardborn: 26 Jan 1883bap: 15 Feb 1883 Anne Janeborn: 03 Jun 1884bap: 01 Jul 1884 Alexander Hamiltonborn: 12 Dec 1885bap: 25 Jan 1886 Elizabethborn: 13 Dec 1887bap: 01 Feb 1888 William Johnborn: 20 Aug 1889bap: 21 Nov 1889
No record found for baptism of Leah, birth index shows fathers name as unknown(illegible perhaps??)
1901 census, Salloon, Magheracross, Co Fermanagh nm=not married, wd=widow(er) M=Methodist Phair Alexander H. nm 14.0 M Salloon Magheracross Phair Annie Jane nm 16.0 M Salloon Magheracross Phair Catherine J. wd 38.0 M Salloon Magheracross Phair Edward nm 18.0 M Salloon Magheracross Phair Elizabeth nm 12.0 M Salloon Magheracross Phair Leah nm 7.0 M Salloon Magheracross Phair William J. nm 10.0 M Salloon Magheracross
1911 census, Residents of house number 2 in Salloon (Bellanamallard, Fermanagh) Catherine Jane, 48, a widow was married for 10 years, had 6 children, all still living at time of census. Only Edward(27) & Leah(17) are still at home.
I would guess that Catherine Jane's surname is Hamilton. There is a Catherine Jane Hamilton married in 1882 in Enniskillen registration district.There are also two William Fair's married in 1882 in the Enniskillen RD.
There is also a Florence Moffitt baptised in the same church, her parents are John Moffitt & Frances, the family are also from Salloon.
Catherine Janeborn: 03 Mar 1880bap:18 May 1880 Elizabethborn: 15 Dec 1881bap: 26 Jan 1882 Frances Helenaborn: 01 Jul 1884bap: 03 Oct 1884 (mother's name Florence, not Frances, but she's in the 1901 census as Lena, so the same family) Florenceborn: 23 May 1886bap: 22 Jul 1886 John Jamesborn: 20 Oct 1890bap: 18 Dec 1890
1901 census, Salloon, Magheracross Moffitt Catherine J. nm 21.0 M Salloon Magheracross Moffitt Florence nm 14.0 M Salloon Magheracross Moffitt John nm 8.0 M Salloon Magheracross Moffitt John wd 50.0 M Salloon Magheracross Moffitt Lena nm 16.0 M Salloon Magheracross
Mother is dead, Elizabeth is not at home.Can't see the family in the 1911 census.