The task is not showing on the record tab

I imagine this is for a process-backed record, yes? That means old records are still referencing old versions of the process which don't have your newer task. If you add a new record, are you able to see the task?

I'm slightly unclear on what exactly you're asking, but in case this helps:

The icon you've circled in your screenshot indicates that the task has been configured as a "Quick Task" by checking the box in the Task Configuration dialog as seen here:

In modern versions of Appian pretty much the only effect this has on a high level is that it prevents that task from showing up in the Task List of whichever user(s) it's assigned to, whether or not the task has been accepted.  (It does some additional stuff if you're dealing with a Process Backed Record, but this is uncommon and confusing functionality which I recommend just be avoided at this point). 

Otherwise, the usefulness of the Quick Task configuration pretty much limited to configuring a task within a Related Action so as it won't show up in the user's task list if they click away without completing it - in such a case it's usually recommended that a timer node end the proecss instance after a certain amount of time elapses without the user taking action on it.