Just poking a little more -- edited to add a couple of references to my earlier post.
Looking around at FS and in the censuses, Sheraton seems to be a very Durham surname with a bit of Yorkshire. I checked Ninian Sheraton (Vivian Theretor!) in the 1841 in Hyson Green, Notts, and he is shown as not born in county. Unfortunately, he died in 1843 so there is no census record showing his place of birth.
There was another Ninian Sheraton of his generation in Durham, born c1786, in the 1841 and 1851 censuses. And there is one in Durham born c1827 (son of James). And earlier, one who married in Stepney in 1756. It's a rather unusual name on both counts, so one does suspect they are all related. And since the one in Hyson Green, Notts, was born out of county, one might suspect Durham was where the John Sheraton father of Thomas and Joseph, and maybe possibly of Caroline, or at least his family, was from.
Aha, varying the spelling at FS (ninian sher*ton), we can account for the c1786 fellow as Ninian Sherraton baptised 1785 Sedgefield Durham. Censuses show him with wife Jane; there is a presumably second marriage for him to a Jane in 1833.
Our fellow in Notts looks like Ninian John Ritson Sheriton who was married to a Sarah and had daughter Sarah in 1798 in Newark Upon Trent, Notts:
https://familysearch.org/pal:/MM9.1.1/JWHZ-ZVKThere are also several Shereston/Sheriston births around that time in the same place in that batch (C06111-1) and three Shereston/Sherriston marriages (C06111-1).
In 1841 there is a Jno Ninian Sherraton (Jno Newion per Anc'y) in Bishopswearmouth, aged 40, unmarried, tea dealer.
FamilySearch has lots of trees for Ninian Sher*tons, but none seem to be for the fellow in Nottinghamshire in 1841.
But one does have a John Sheriston baptised 1805 Newark Upon Trent, son of William and Sarah (one of the ones in batch C06111-1 mentioned above):
https://familysearch.org/pal:/MM9.1.1/JQ5F-G31I would have wondered whether William was a misreading of Ninian, but it's consistent across several records in that batch. Mind, that could be a transcriber's consistent misreading. Those records are consistent in time/place with the record of Sarah daughter of Ninian John Ritson Sheriton and Sarah in the same batch.
A load of people seem to have a Phoebe Sheraton born c1800 in Notts in their trees at Ancestry/Mundia, married to William Hopkin and living in Radford in 1841, but don't have parents for her. In fact, she is in Hyson Green, district 4.
According to at least one tree, that Ralph Sheraton was born in Portsea 1795, son of Ralph 1773 born in Stockton on Tees. Some of Ralph Jr's kids seem to have ended up in Canada and the US.
Aha. Ralph Sr 1773 was a brother of Ninian John 1768 -- who, the tree says, had a son John Sheraton, about which it has no info. But Ninian John's other kids were Sarah and Thomas, and their mother was Sarah, so I think probably that "William" at FS was really Ninian indeed.
And that John Sheraton would really be of an age to be the father of Joseph and Thomas (from the 1841 censuses, baptism records posted earlier) -- and possibly of Caroline Spencer ...
