how to monitor the file share witness and cluster is online?

If there are an odd number of DAG members, there's absolutely nothing to monitor because the FSW isn't used.  If there are an even number of DAG members, you can enter:

Get-DatabaseAvailabilityGroup -Identity DAG_NAME -Status | FL

We can monitor the DAG using the below command.

Get-DatabaseAvailabilityGroup -Identity DAG -Status | fl

The other option is using the Cluster Manager(Fail over Cluster manager) console.

If its even number of members in DAG we can see the FSW details.In case you have odd numbers for member it should not reflect in the console.

The below article will have the details when DAG's need the File Share witness.

https://www.credera.com/blog/technology-insights/microsoft-solutions/when-do-dags-need-a-file-share-witness/ 

it have other way to monitor?

thanks..

There is no other option to monitor the File Share Witness.

Please propose as answer