Jessup has been referred to in ufological circles as "probably the most original extraterrestrial hypothesiser of the 1950s", and that he was "educated in astronomy and archeology and had working experience in both."  Actual evidence of an educational background in archaeology, or archaeological field work, is absent from Jessup's resume, but Jerome Clark  reports that Jessup took part in archeological expeditions to the Yucatan and Peru in the 1920s.

Jessup achieved some notoriety with his 1955 book, The Case for the UFO, where he argued that unidentified flying objects represented a mysterious subject worthy of further study. Jessup speculated that UFOs were "exploratory craft of 'solid' and 'nebulous' character."  Jessup also "linked ancient monuments with prehistoric superscience," years before similar claims were made by Erich von Däniken in Chariots of the Gods?.

Jessup wrote three further saucer books, UFOs and the Bible, The UFO Annual (both 1956) and The Expanding Case for the UFO (1957). The latter suggested that transient lunar phenomenon were somehow related to UFOs in earth's skies. Jessup's main saucer scenario came to resemble that of the Shaver Hoax perpetrated by science-fiction magazine editor Ray Palmer --- namely, that "good" and "bad" groups of space aliens were meddling with terrestrial affairs. 

Like most of the writers on flying saucers, and the so-called contactees, that emerged during the 1950s, Jessup displayed familiarity with the alternative mythology of human prehistory developed by Helena P. Blavatsky's cult of Theosophy, which included the mythical lost continents of Atlantis, Mu and Lemuria.