Lots of things could be wrong. Your mail handler might not be properly configured, you may have mail filter problems. Give us a bit more details about how you configured the mail integration, the documentation you used, the attempts you made to fix it etc.
I used for configuration this article
When test connection to email there is no error, said that everything ok. But email doesn't come to service desk. Not from customer email, not from another.
There is a good doc on troubleshooting email channel problems in the link below which could help you:
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