How to deal with supervisor accusing me of not completing work?

a matter that they think doesn't matter

That is only half true, unfortunately. They think the work matters (or whether they find it or not), but your feelings don't.

If you have a backup for a job, then things are easier (if you happen to lose this one). If not, you are in a very weak position for negotiation.

Obviously, they have an emotional behavior (unprofessional), so you cannot reason with them much.

The way I understand things, an easy way to make things better with little effort and little risk - is to send a notification (by e-mail, or other means) after every delivery of work. It can a delivery of one document, or of more documents. Just keep it simple, something like:

Dear Mr/Mrs ...

I finished working on .... Please find the files at the following links:

Link to folder: ( link )

Link to File 1: ( link )

Link to File 2: ( link )

...

Best regards,

( Name )

( signature (if applicable) )

In that way, they only need to click on the link to have their data. Please note that it is better to provide the file name separately from the link, for better clarity. Sometimes, the links become unreadable after the proper encoding and cleaning.