What is the correct adjective corresponding to the noun Venus?
Venus is both a planet and the Roman goddess of love and sex. Adjectival forms therefore have two separate uses: for the planet, and in medicine to describe things like sexually transmitted diseases.
"Venusian" is by far the most common adjective in use for the planet among professional astronomers. Some classically minded writers dislike "Venusian" because it doesn't resemble Latin forms such as "Veneri." "Venerian" was used by some 20th-century science fiction writers such as Robert Heinlein and Jown W. Campbell, Jr. It also appears to have been used sometimes as an adjectival form of Venice (George Finlay, History of Greece Under Othoman & Venerian Domination). "Cytherean" is sometimes used, referring to the island Cythera, near which the goddess was supposed to be have been born. A search of astronomy papers on arxiv.org, however, shows that "Venusian" is nearly universal.
In medicine, the most common term is "venereal," which is closer to being a legitimate Latin form than "venusian." There are also "veneric" and "venerean."