They are characteristic of Prunus leaves (cherries, plums, gages).
Having the leaves somewhat in tufts would be right for some cherries.
Because I can't see any petiolar glands, because of the pattern of the veins and marginal toothing of the leaves, and the nature of the bark, I lean towards apple. There are lots of crab apples or similar-looking species, differing in size of tree, size and colour of fruit, and other things. It would be difficult to ID the species/cultivar.
The key thing to do is cut open a fruit: if it has one kernel, it is a cherry; if it has multiple pips it is a crab apple. Please let us know!
Whichever it is, the fruit is probably edible (test that only at your own risk). I say that because it appears the tree was grafted (at the top of the stright trunk), and that's most likely to be done on a domestic fruit tree.