Learn Turkish: Bu muska bizi cinlerden koruyacakmış. - Apparently this amulet will protect us from jinns.

The word koruyacak simply means "it will protect". By adding the inferential suffix -mış, you get koruyacakmış, which translates to "apparently it will protect" or "I heard it will protect." You use this combination when you are talking about a future event based on hearsay or something someone else told you, rather than stating it as a known fact.

What is the root of koruyacakmış and why is there a -y-?

The verb root is koru- (to protect). Because this root ends in a vowel and the future suffix -acak begins with a vowel, you must insert the buffer letter -y- to connect them smoothly, creating koruyacak. After that, the -mış suffix is attached.

Why are there two different noun cases used for bizi and cinlerden?

The verb korumak (to protect) requires you to mark the object being protected with the accusative case, which is why the pronoun biz (we) becomes bizi. Meanwhile, the thing you are being protected from takes the ablative case -dan/-den, which is why cinler (jinns) becomes cinlerden.

Why is it -mış and not -miş at the very end of the verb?