This sounds like a deposition of a party. So you will not be using a subpoena duces tecum. Instead you use the deposition notice, and in that you can request the production of documents.
The better approach is probably to make a separate demand for inspection of documents and other tangible things and then take the deposition after the document production. That gives you time to review the records in advance of the deposition, and you can probably conduct a better examination with the additional preparation.
If that is not feasible for whatever reason, and you have a problem with what was produced at the deposition, I would: try to take as much of the deposition as possible, perhaps inquire as to what documents you requested exist, why they were not produced, then continue the deposition to a future date and try to have the documents produced in advance of the follow up session for the reasons mentioned above.
If that doesn't work then you are probably looking at a motion to compel. You need to meet and confer in advance to try to work it out. You can claim expenses associated with bringing the motion. If you had to cancel the deposition then maybe you can get the reporter's fee. I would not look at a discovery motion as a way to come out even or ahead on the litigation expenses. You will be better served to try to act in a reasonable and practical fashion.
Discovery motions can be tedious to bring. You'll probably want to consult with an attorney about strategy and tactics for your particular case and the best way to approach this in the context of your overall litigation goals.
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