If I clear customs in Italy and get a Schengen stamp, will I have to go through customs again in another Schengen country if I enter by air?

I'm planning to fly from Rome to Malta for a couple days, and I was curious if I'll have to clear customs in Malta again, since I'll already have a Schengen stamp issued in Italy?

I did fly from Denmark to Poland once after leaving the airport to sight see, but that was almost 10 years ago, and I don't remember if I had to go through customs in Poland again or not.

I have an American passport.

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If I clear customs in Italy and get a Schengen stamp, will I have to go through customs again in another Schengen country if I enter by air?
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