How to release datasets with fingerprinting
"Digital watermarking" is a set of techniques that might be useful in this context.

From the wikipedia page:


  "Watermarking" is the process of hiding digital information in a carrier signal... Digital watermarks may be used to verify the authenticity or integrity of the carrier signal or to show the identity of its owners. [Emphasis added]


To address your requirement, you would insert a unique watermark for each client that receives your data. Watermarking techniques address requirements such as robustness to modification and imperceptibility.

As an example, this paper talks about watermarking numerical data: "Watermarking Numerical Data in the Presence of Noise", pdf