Dates, coconuts, acai berries and palm oil grow on palm trees. All are rare in local home gardens. The palms that are popular in much of California are almost exclusively ornamental. Very few of them produce useful fruits. Despite the similar pronunciation, such palms are not at all related to pomes. Some of the more familiar fruits happen to be pomes, which are also known as pommes.
Apples and pears are the most popular examples of pomes. Quinces, which were very popular decades ago, are now rare. Quinces are so closely related to pears that they work well as dwarfing understock for home garden pear trees. (Orchard pear trees use other understocks that are not dwarfing.) Actually, most quince trees grew secondarily from roots of dead or removed pear trees.
Saskatoons (serviceberries), chokeberries (aronias) and medlars are locally rare pome fruits that are slowly gaining popularity. Productively fruiting cultivars of loquat are now more available than those that were primarily ornamental. Some flowering quinces may produce a few small fruits. Mayhaws and mountain ashes (rowans) are berry-like pomes that are more familiar in other regions.
The earliest cultivars of apple might be in season by late July, before stone fruit season finishes. (Some peaches, the largest of the stone fruits, ripen in September!) The latest will be ready in late November, at least a month into citrus season. Pear season extends from August into October. So, this is the middle of apple and pear season. Most but not all other pomes are already finished.
Like stone fruit trees, the trees and shrubs that produce pomes need very specialized pruning while dormant through winter. Without annual pruning to enhance structural integrity and concentrate resources, apple and pear trees are unable to support all of their fruit. Shrubby quince trees become thickets without pruning for grooming and confinement, although they may not need it annually.