This is indeed a mystery - like you Monica, I can't find any birth records for James Clelland McFadyen or Anthony McFadyen - nor any conclusive evidence of Alexander McFadyen existing before he appears on the 1859 marriage record.
However, I have a somewhat radical theory, but to follow it through, we need to return to the parents of Christina Brown - James Dewar Brown and Agnes Beveridge...
James Dewar Brown married Agnes Beveridge in 1835 - the banns were called in Airdrie, Lanarkshire, and Newton, Midlothian. James was residing in Airdrie, and Agnes in Newton. This couple had a daughter - Isabella Harper Brown - baptised at the United Secession Church in Airdrie on 12 Feb 1837 (b. 24 Dec 1836) - both parents are named.
There is also a Christina Brown who was baptised at the United Presbyterian Church in Dalkeith, Midlothian on 11 Aug 1839 (b. 1 Jul 1839) - the entry simply reads: ‘daughter of Brown, Easthouses…’ so impossible to know if this is our Christina, although the age and location appear to potentially match. There are several Brown families in Easthouses in 1841 - all miners - but none of them are James, and none have a daughter Christina, although the child could, of course, have died in infancy.
As mentioned previously, this appears to be our Brown family in 1841 in New Monkland. Note that all the family, aside from Isabella, were born outside Lanarkshire.
1841 New Monkland, Lanarkshire
James Brown, 30, coal miner, Scotland
Agness Brown, 25, Scotland
Isabella Brown, 5, Lanarkshire
Christina Brown, 3, Scotland
James Dewar Brown appears again in the 1851 census in Old Cumnock, Ayrshire, as a widower, and with (apparently) another daughter named Elizabeth. So it looks likely that Agnes Beveridge died between 1841 and 1851.
1851 Old Cumnock, Ayrshire
James Dewar Brown, 40, widowed, coal miner, Edmonston, Midlothian
Elizabeth Brown, 14, daughter, Ruthin, Midlothian
Is 'Elizabeth' Christina? I can't find another obvious candidate for Christina in 1851, but neither do I have a positive sighting of Isabella (although there is an Isabella Brown of a suitable age and birth location working as a servant in Dunipace, Stirlingshire).
By 1861, James is in Whitburn, West Lothian, and Isabella is back with him:
1861 Whitburn, West Lothian
James Brown, 52, widowed, ironstone miner, Edmonston, Midlothian
Isabella Brown, 25, daughter, Airdrie, Lanarkshire
Alexander Cameron, 23, boarder, ironstone miner, Edmonstone, Midlothian
Christina Cameron, 23, boarder, Edmonstone, Midlothian
James Cameron, 3, Old Cumnock, Ayrshire
I’m intrigued by the ‘Cameron’ family who are lodging with James and daughter Isabella. They are the right age and occupation to be Alexander McFadyen, Christina Brown and their son James Clelland McFadyen - what intrigues me is that Cameron is the maiden name of Alexander McFadyen’s mother, according to his 1859 marriage.
I can’t find any record of a marriage between an Alexander Cameron and a Christina/Christian - nor was there a James Cameron born in Old Cumnock to an Alexander Cameron and Christina/Christian.
However, there is a James Brown Ferguson who was born in Old Cumnock in 1858, the illegitimate son of David Ferguson and Christina Brown. David Ferguson married Jane Burns, with whom he had six further children, about two weeks before his illegitimate son was born, but this child doesn’t appear with his family in any subsequent censuses - and he doesn’t appear to have died in infancy, as I can’t find a death registration.
So… my theory is that Christina Brown’s son James Brown Ferguson could be the child that became James Clelland McFadyen - and may also be the James Cameron who appears in the 1861 census in Whitburn. Clearly I have no conclusive evidence to prove this - but neither can I find any conclusive evidence to disprove it….
Ruth