Pixiu is an Inbox and notification app for Gmail on macOS. With this program, you can view inbox snippets and incoming e-mail notifications on your menu bar. In the settings window, you can make some changes, such as pause/resume the syncing, change the syncing interval, feel free to revoke, start on login, and turn on/off the notifications.
Mia for Gmail (was Notifier Pro for Gmail) is a desktop Gmail client which sits politely in your menu bar.