How do I say "Switzerland's"? Der Apfel von der Schweiz or Der Apfel der Schweiz?
"der Apfel der Schweiz" is a proper genitive construction, but genitive struggles to stay 'alive'. So it is correct, but in certain social groups you wont hear it.
"der Apfel von der Schweiz" is a somehow proper construction, it replaces the genitive construction above and is more common than the one above. It may be considered bad style, but its accepted as proper german since a few years. So you will hear this more often, yet if youve an oldfashioned or just a very strict teacher, then he might still mark it as mistake or at least a stylistic mistake.
Not said by you, but already mentioned by others.
"der Schweizer Apfel" is also a common way to express it, yet it is an adjective construction. So to describe it in english. the apple of germany = germany's apple but this third option is the german apple.
I'd go for "der Schweizer Apfel", which is equivalent to "der deutsche Apfel / the German apple". In the same way: "Schweizer Käse / Swiss cheese".
For "the apple from Switzerland", it would be "der Apfel aus der Schweiz".
"der Apfel der Schweiz" means there's only one apple "of"/in/from Switzerland, like "die Hauptstadt der Schweiz / the capital of Switzerland", "der höchste Berg der Schweiz" (highest mountain); or for the entirety of a number of things (although "Schweizer" would sound more elegant): "Die Züge der Schweiz sind immer pünktlich" ("The trains of Switzerland are always on time").
"von der Schweiz" is just a colloquial way to say "der Schweiz" (genitive).