Where does “しゃ” come from?

しゃ (Middle Chinese) comes from Old Japanese 汝, from Old Japanese れ — nominalizing suffix used to form pronouns, often from demonstratives: one, thing.

Ancestry of “しゃ”, step by step

StepLanguageWordMeaning
1Old Japanesefirst-person singular pronoun: I, me;...
2Old Japanesenominalizing suffix used to form pronouns, often from demonstratives: one, thing
Every word from Old Japanese Every word from Old Japanese