Do we really need a file share witness? We have an Availability Group configured. Total number of nodes in the cluster is 3 (odd). All are in same subnet. Also we do have file share witness. Everything is working fine for now.

My question is: do we really need file share witness? And what should the ideal quorum configuration be?

As per my knowledge, it is not needed as we already have an odd number of nodes, so node majority quorum configuration should be fine and is recommended.

SQL Version: Microsoft SQL Server 2016 (SP2) Enterprise Edition
OS Version: Windows Server 2016 Standard
In my opinion , based on version of windows you have and especially using always on configuration i would recommend having a quorum configured. In your case its File share which seems OK or else you have the option of quorum drive witness.

More on this is very neately explained by @Brentozar here


  You don't have a choice as to whether or not to have quorum: Always On
  Availability Groups are built on top of Windows Server Failover
  Clustering, which requires quorum voting to understand who the primary
  is for a given AG at a given time.
  
  I think what you might be asking is whether or not you need an
  old-school quorum drive (like a Q drive on a SAN). These days, Windows
  Server Failover Clustering (WSFC) can either use a quorum drive
  witness, OR a file share witness.
  
  Windows Server 2012 R2 includes dynamic witness capabilities: if you
  have an even number of voters (like if 1 of your 3 cluster nodes goes
  down), then Windows will automatically add in your witness in order to
  be a tiebreaker. That's why you want to configure the witness (either
  a disk or a file share) ahead of time - Windows will automatically
  manage its voting rights whenever you have node failures or network
  failures.


Also refer to another part of the answer which should help you here


  In a 3 node cluster you can setup node majority as your quorum mode
  and then you can survive the failure of a single node within the
  cluster . That is in most cases sufficient. If your cluster spans
  multiple sites you might want to fiddle with the quorum-vote weight
  depending on your failover plans