there is a possible baptism on 8th november 1797 with a mother 1st name as alice no other information on parents
One of the 1797 baptism images gives this info --
Anthony, son of Alice Norris,
spinster, Ingerthorpe
However, another image gives the location as Markington.
Both are near each other, and close to Harrogate.
The 1851 census gives his birthplace as "Marton" which is northeast of Hull.
ADDED1801 - An Alice Norris (of Ripon) marries a John Pearson (of Kirkby Malzeard)
If we have the correct baptism and mother then I wonder if Anthony's birthplace/childhood home is MASHAM (not Marton, which the enumerator may have heard incorrectly).
Masham is just north of Kirkby Malzeard, and is a better fit for the area in question.
Having said that, there's an 1806 baptism for a Sarah Elizabeth Pearson in Hull. Parents - John and Alice.