Phegeus was a king of Psophis in Arcadia, and the father of Temenus, Axion and Arsinoë. The only Greek word closely resembling his name is phegos, 'esculent oak', i.e. one whose fruit could be eaten (compare Aesculapius).
We do not have a specific reference to such a tree or fruit in the stories about him, but doubtless there could be a connection with some ritual or religious ceremony, perhaps on the lines of those associated in other western mythologies with the mistletoe (which also grows on oak trees).