There are some varying views among ulema on these matters, so if you have a genuine interest in pursuing parapsychology research and would like a solid fiqh view, it is good to sit down with a jurist and discuss your plans.

Hiring someone to perform a work adds another dimension to the fiqh discussion since it falls under the subject of transactions, and so you should discuss whether or not it is considered a legitimate or allowable transaction according to that jurist. There are certainly different scenarios one could envision, e.g. hiring someone who asserts they are psychic and depending on their personal perceptions is a different sort of transaction from hiring someone to operate some sort of sensor equipment or special camera.

There may also be some ethical considerations. For instance, seeing as most human beings do not like to be the subject of scientific research without their permission, possibly some jinns feels the same way. These things might sometimes be discussed as well.