Frank
Well, I think I've found what you're looking for, but I nearly missed it.
I took the precaution of checking the register for several years from 1781, rather perturbed that I couldn't find either James or any Ramseys. Then I found the following - and I must say, you're lucky, because this section is part of the "Dade" register:
Edward son of John Ramsey, cordwainer, who was the son of William Ramsey of Eastrington by Mary, daughter of John Rook of Holme-upon-Spalding-Moor. His wife was Eizabeth, daughter of Thomas Hicks. (I think both Rook and Hicks were farmers). Edward was born on 16 Nov, bapt 26 Nov. The year is unclear, but seems to be 1789 (someone seems to have inserted a missed entry for 1787 on the previous page, but it interrupts the flow of the months. The following year is 1790).
I carried on looking for several more years and after a second check, I found on the same page:
James Ramsey, son of Edward Ramsey, cordwainer, 5th son of William Ramsey (see above). Edward's wife was Elizabeth, daughter of Thomas Brown of Haltfield Wood House - that's what it looks like - and Susanna, daughter of James Witter of Sheerness in Kent, mariner, by Sus: daughter of ? Hepworth/Hopwood, something like that, of Chatham. Born 21 Oct, bapt 27 Oct. Again, this would be 1789, so I can only think he was a bit confused about his birth date.
I checked the local early OS maps for "Haltfield Wood House," and then the internet. And there is a Hatfield Woodhouse near Doncaster, which may be what you want.
You may be interested to know that in the 1820s, a James Witter was the landlord of a pub in North Cave - he appears several times in the ERY archive catalogue. You could also see if Hull History Centre's catalogue has anything on Witter, as lots of mariners are listed.
All the best.
Joyce