When is it appropriate to use “by accident” in a sentence?

Question by Paola: When is it appropriate to use “by accident” in a sentence?
I’m more comfortable with using the phrase “by accident” but I’ve noticed that people also use “on accident.” Such as in the sentence: “Even Tom only found out on accident.” When is it appropriate to use by accident, and on accident? Are both appropriate to use? Any help is appreciated.

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