To look for a Users owned files, use the Drive audit and apply the query builder.
Set the Search Type to – User/Group/OU Search.
Enter the user’s email address and set Ownership to ‘Owned’, otherwise, it will bring up files he has access to as a reader, editor or owner.
This will find all the Files where the selected user is the Owner.
Alternatively, to find files owned by a user you can use the Simple Filter type in Drive Audit. Click on the ‘Apply Custom filters’ button and search for Owner = username.
The results from both searches will be the same. A quick overview of the result can be opened by selecting “Show stats for the current filter”.