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Derbyshire Record Office has an apology displayed because the online catalogue is not functioning properly at present.  They have other records for the Archdeaconry of Derby. All the records for the Diocese of Derby should be in the designated record office - Church of England rules.

CORRECTION: I have now found this in Derbyshire's guide to parish records:

STRETTON-EN-LE-FIELD
Parish originally included part of the township of Oakthorpe. Transferred to Leicestershire 1897, and now in diocese of Leicester.

a twitten... in Sussex

Interesting that bears out the Dialect Dictionary.  As g eli says, counties around Derbyshire, but then the dictionary suggests a sneaky line through eastern England, somehow reaching Sussex.

Whitby, North Yorkshire has narrow alleyways, generally leading down to the river/harbour, known as ghauts

Whitby seems closer to snicket country but this is something different.  The Dialect Dictionary gives it under Gaut, a water channel, a mill-wheel channel OR a narrow passage.
https://archive.org/details/englishdialectdi02wrig/page/580/mode/2up

Now, suddenly I recognise that word as Goit, a mill-wheel channel.  There were scores of them around Sheffield, where five rivers converge with numerous mills forging and grinding metal goods.  It does not appear in the Dialect Dictionary with that meaning, only as a way or a road. (In Scotland, from Norse.)

but we'd just as often say snicket

My mother used snicket - I'm not sure where she acquired that from.  Having read all this I would say possibly her grandmother from Cleckheaton.

The standard 19th cent. F was formed exactly the same as the T, with the addition of a small cross bar with a loop, across the centre.  (It was still being taught in British primary schools in the 1950s.)  This looks like a cross bar running into the r.

Oops, sorry!

These two maps cover Oulton, West Riding, sheets 233, 234:

https://maps.nls.uk/view/102345004
https://maps.nls.uk/view/102345007

The sheets to the north are mostly Woodlesford, numbered 218, 219.

I cannot see any tithe award in Genuki, but there were two enclosure awards listed under Rothwell etc. dated 1793 and 1818.  They are listed in Yorkshire Enclosure Awards by Barbara English, 1986, p119.
At that time they were in the hands of the parish and Rothwell UDC but probably at West Yorkshire Archives by now.   Worth enquiring, also ask about tithes.

That is, if you do not find any other solution to this.

? Three Cornered Piece? - a field name?