What is the prefix para mean in these two job titles?

here

Para- is a prefix that translates from the Greek as “beside or along side of”. Given that definition, I would say that in the two words you mentioned that they fall next to the noun that you list. They are like those things, but aren’t exactly them.

In your first example, parapsychology, I would say it is being used in the sense of “beyond” or “past” possibly as an abbreviated version of the adjective modifier paranormal. In paranormal it would certainly be being used to describe states beyond normal.

In your second, paramedic, I would say it is being used to convey an occupation that would be considered ancillary or supplementary to the medical field. It could be being used to indicate a subordinate position in the medical field. I’m not sure if I agree with the designation and I am not sure why they would not be considered a “medic” since, in my opinion anyway, they are performing the same services as those provided by a medic or corpsman in the military.

@rojo Your words ancillary and supplementary are very helpful. A parapsychologist in my line of work is often a person who receives mental health care and has been trained to work with his/her peers, others also receiving mental health care. They are not clinicians like a psychologist is. They are people with lived experience of mental illness who are trained to provide support to their peers.

@Hawaii_Jake‘s link does a good job of suggesting what the words mean. The original use was to mean along side of or supplemental to. That would cover paramedic. The use was extended to mean beyond, which would cover parapsychology and paranormal. It can also mean abnormal as in paranoia. Here is a short summary