The source in where I studied told me that you mark the object of potential form with が particle instead of を particle because potential form is just a state, no actual action is taken. It specifically told me that を can be used but が is better. I know how to make sentences where I'm the subject. 山が登れない : I can't climb the mountain. 彼が言っていることが聞こえない : I can't hear what he is saying. But what if I want to say "He can't eat apples" or "Alice can't go to school" or even "Bob can't kill Tanaka". With が、を、は I could be mistaken in saying "Tanaka can't kill Bob" instead of "Bob can't kill Tanaka". Can が also denote the subject or only the object?

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The particle you are looking for is に.

He can't eat apples.
≒ 彼はりんごを食べられない。
≒ 彼にりんごは食べられない。

Bob can't kill Tanaka.
≒ ボブは田中を殺せない。
≒ ボブに田中は殺せない。

He can't climb this mountain.
≒ 彼はこの山を登れない。
≒ 彼にこの山は登れない。

the reason why he can't climb this mountain
≒ 彼がこの山を登れない理由
≒ 彼にこの山が登れない理由

He can't hear what I am saying.
≒ 彼に私が言っていることは聞こえない。
≒ 彼に私の言っていることは聞こえない。 (ga-no conversion)

Alice can't go to school.
(You cannot say アリスに学校に行けない. Probably because there is already に?)

(Different words are topicalized using は, but I don't know which is "better"...)

EDIT: changed the fifth example above for consistency.

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