George Shields Mofat
Born May 14th 1849...Myles Farm, Tranent, Haddingtonshire, Scotland
Son of James MOFFATT and Joan POW
At first sight this may look like Peter's reputed father has a lot of answering to do - but I don't think so....
George Shields MOFFAT is the 3rd child, (and 2rd Son) of James & Joan - and he appears to be legitimate born.
James MOFATT's father is named David, his mother is Janet,
Joan POW's father is named George, her mother is Isabella.
In the 1851 Census, James and Joan and their 3 children, David, Isabella and little George are indeed, at Myles Farm. James is an Ag Lab - likely in the employ of John SHIELS.
James & Joan named:
their first son David - after James father.
their second Son George - after Joan's father (and perhaps a middle name 'Shields' after their 'laird', quite a common Scottish thing to do if there was a strong loyalty and respect between worker and employer)
their first daughter Isabella after Joan's mother
their second Daughter Jessie (pet form of Janet) after James' mother.
Google "Scottish Naming Patterns" - it's a very useful tool with Scottish research, not always foolproof but very visible and fairly strictly adhered to in many a family, more so than with English families. It can and did create families with generations of the same names passed down, and with little parcels of cousins running about in the same parish, all named the same after their mutual grandparents

What helped sort them out, was the other common practice, to give a mother's or grandmother's maiden name as a middle name!
To keep the overall pattern, the 3rd Son should be named after his father - ie James (the 3rd son is Robert James, a slight deviation) . And the 3rd Daughter after the mother - ie Joan (which can be also rendered as Jean, Johan, Johanna, Johan ) in records - perhaps "Jessie" covered both Janet and Joan!
So - I've gone all round the world to say is.... I would bet this George Shields MOFFAT has nothing biologically to do with Peter's reputed father.
Good find though!
Cheers
AMBLY