We are often confused by these words or phrase. If we know the difference, then it's more easier to choose the right one.
Except usually subtracts: it is like saying without, or minus.
I like all musical instruments except the violin.
Besides adds: it is like saying with, or plus.
Besides the violin, she plays the piano and the flute.(sha plays three instruments)
Apart from can be used in both senses.
Apart from the violin, she plays the piano and the flute.(= Besides the violin…)
I like all musical instruments apart from the violin.(= except the violin)
There is only one case that these three words or phrase have the same meaning, when after no, nobody, nothing and similar negative words.
He has nothing besides/except/ apart from his salary.(only has his salary)