What is Jus Tertii?

Legal Definition
Jus tertii (Latin, “third party rights”) is the legal classification for an argument made by a third party (as opposed to the legal title holder) which attempts to justify entitlement to possessory rights based on the showing of legal title in another person. By showing legitimate title in another person, jus tertii arguments imply that the present possessor’s interest is illegitimate or that the present possessor is a thief.

Under United States law, jus tertii arguments are generally insufficient to support actions for replevin because they fail to show that possession is more legitimate in the third party than in the present possessor. However, a bailee or other legal agent of the owner may successfully assert the argument.

The principle is sometimes used to allow one person to enforce or test the constitutional rights of another, which usually can't be done due to lack of standing. This is only possible for fundamental rights, where there is a close connection between the person whose rights are violated and the person wishing to enforce them, and the constitutional right being enforced is a fundamental right. See, e.g., Singleton v. Wulff Et Al., 96 S. Ct. 2868, 428 U.S. 106 (U.S. 1976).
-- Wikipedia
Legal Definition
The right of a third party.
-- Ballentine's Law Dictionary