Quality Corner wasn’t in Hexham itself. It was on the north side of the River Tyne in the Parish of Warden.
It appears as ‘Quality Corner’ on all the censuses up to and including 1881, but by 1891 appears as ‘Quality Cottages’.
You can see it on this ‘side by side’ map https://maps.nls.uk/geo/explore/side-by-side/#zoom=16.8&lat=54.99098&lon=-2.14612&layers=168&right=ESRIWorld
And as a bonus there are photos here! https://www.geograph.org.uk/photo/94319 and https://www.geograph.org.uk/photo/1664788
Jennifer Britton