Oxyphil cells are a specialised group of cells found in the ParaThyroid gland of humans (and some other mammals).
They're not present at birth, and their numbers increase with age. They also increase in patients with chronic kidney disease.
Various research projects suggest that the cells secrete Parathyroid hormone-related protein (PTHrP) - a hormone which is known to be involved involved with bone-growth regulation.
But their overall function is completely unknown. The cells have large number of mitochondria, suggesting they may have a role in energy production.
Further details, see : J Clin Endocrinol Metab. 2012 Aug; 97(8)