In the end of 2019, Google began to require verification of applications that use Google API for accessing user’s data. Verification process took several weeks and in the last weeks new users who tried to install application received the error This app isn’t verified.
Now the issue is resolved for AweSync app. Sorry for inconvenience!
BTW: AweSync.Mail is still being verified. But you can use the following FAQ to install the app – App hasn’t been verified by Google yet