Hello Eliza
These come from St Leonard's parish records. I only use parish records as these are the most reliable source, although errors occur even in them.
The first James could well have been the father of John & Edward but I was raising the query that there were two James by different mothers, casting a degree of doubt as to who the father of John and Edward was. The James by Francis Gamon's wife may have gone by the name Gamon or by Newton - it depended on who brought him up, I imagine.
Looking at the records again, there was a James Gammon baptised in 1784 but his parents were William and Jane, not Francis' wife, the mother of the illegitimate James.
Regards
AJ