  We prove an analogue of a theorem of A. Pollington and S. Velani ('05),
furnishing an upper bound on the Hausdorff dimension of certain subsets of the
set of very well intrinsically approximable points on a quadratic hypersurface.
The proof incorporates the framework of intrinsic approximation on such
hypersurfaces first developed in the authors' joint work with D. Kleinbock
(preprint '14) with ideas from work of D. Kleinbock, E. Lindenstrauss, and B.
Weiss ('04).
