When I want to update the game in the itch app, an error occurred which warned x509: certificate signed by an unknown authority. So, I want some help to solve this problem, please. 

Does this happen consistently for every game? Can you confirm that the clock on your computer is set correctly. We aren’t aware of any widespread issues with any of our certificates, and given that an individual’s computer can be in a wide range of states, it’s hard for us to offer more help other than suggesting you disable any third party software that might be interfering with your network connection (this includes virus and security software, as they can often be overzealous about what they block).

Hope that helps