Messages

Do you have iMessage enabled on the Mac? If so, try logging out as outlined below.

With the Messages app open, at the very top menu bar, click Messages.

Choose Preferences from the drop-down list.

Click Accounts.

Find your Apple ID on the list with the iMessage icon. Click on it.

Uncheck Enable this account or select Sign Out.

Doing so will log you out of iMessages. Close the app, and you’re done; you will no longer receive iMessage notifications on your Mac.

Now quit Messages and try enabling it again. You can try a test message to yourself.

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