I am assuming the question is 'Who are J.P's children?'
I found one born in Scotland and one in Camden, South Carolina, USA.
On 'MyHeritage' there are several American J.P.'s with only one child and there are two date ranges:
John Caldwell Pinkerton (1779 - 1843) OR (1779-1851)
More information about J.P. would be helpful.