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Hi @Cathal Condon ,
Per my test, this requirement can be directly realized in the list, you can go to the list settings> Advanced settings>Read Access:
As far as I know, there is no such setting in the Document library. If you have the edit permission, you can set who can view or edit the Item through Manage Access. However, this method may not be very convenient if there are many files, and it may also affect Performance.
Another way is : Enable Draft Item Security.
If you enable Content Approval on the library, you have the option of limiting draft visibility to only approvers and the item author. However, as soon as a document is published for all to see, the library's permissions will apply as normal.
Here is an official document you can have a look:
https://support.microsoft.com/en-us/office/require-approval-of-items-in-a-list-or-library-cd0761c4-8c3f-4ea2-9435-13c28aa23d08
In your case, maybe you can do not give this user permission in this site, create a separate library, share with the user and then give him unique permissions in this library. If you need to synchronize files to other libraries, you can use flow or manually transfer.
Similar post for your reference:
https://social.technet.microsoft.com/Forums/azure/en-US/089f997a-e4fa-43ab-9ba0-a983b80940d6/how-can-we-force-a-user-to-only-edit-the-document-that-he-has-submitted?forum=sharepointgeneralprevious
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