Atoms: Protons, Neutrons, & Other Particles?

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Just one quick question I couldn't find an answer on the internet to, after a long search.
We are taught that atoms are made from protons, neutrons and electrons only. There are many other leptons and hadrons existing, but where are they in this story?
 
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Okay, so in a usual atom, only protons, electrons and neutrons exist. But how are those exotics produced?