That is a pollination problem: you can confirm it by slicing the apple in half and see how many seeds are present and how developed they are. If there are few, or even no, poorly developed seeds you have a pollination problem.
People tend to think of pollination in binary terms: yes/no. And we often assume that since the trees have been sold as "self-fertile" they will simply bear fruit like that. The reality is far more complex and for multi-seeded fruits, like apples and pears, make it doubly so.
Pollination is a very complex operation that takes into account rain, wind, pollinator (bees, bumblebees etc) density, air temperature and genetics.
Anna is an apple cultivar that blooms very early in the season: this means pollination can be affected by cold spells, rainy weather, lack of bees but, far more critical, lack of a compatible pollenizer.
At this point you may ask: hold on a minute. Why do I need a pollenizer? My tree is self-fertile and swarming with bees. It indeed is. But as said before pollination in multi-seeded fruits is very complex: you need both a high amount of pollen and genetic compatibility to have proper seed (and hence fruit) development. Otherwise your tree will indeed set fruit, but they will be malformed, like you've seen, and/or tasteless, which is a complete calamity for commercial growers.
How do you solve this problem? Very simple: look for an apple cultivar named "Dorsett Golden", buy one and plant it near your Anna. These two apple cultivars not only bloom at exactly the same time, but also have perfect genetic compatibility with one another, meaning they will readily pollenize one another. Both cultivars were developed to be grown in hot or even tropical climates (Anna in Israel and Dorsett Golden in The Bahamas) so they can handle the heat no problem.
