Is there a way to show how many times a record has been updated/modified by user?

Are you trying to watch for any/all changes?  Or, is there one field in particular that you are looking to track? i.e. a Status change, or a date change, etc.

If you want to log any and all changes, you are going to have to create a "Modified Log" table.

Then use the new "QuickBase Actions" functionality to create a record every time the main record changes.

You will have to re-create all the fields that you want to track, and then format the 'Action' to copy all those fields to the new record.

Honestly, its a bit nasty, and might not be worth it.  You can also do this with script to create the log records.

If you wanted to just target the changes to just a few fields, I'd recommend a simpler version of the "Log" table, to just pay attention to the key fields.
You could even make those changes a smaller table, and allow a button push to create those changes.