The word Usian is one of the many attempts to create an adjective--specifically, a demonym--for United States nationals, as an unambiguous alternative to "American", which is the term usually used. Mentions of the word, and proposals to use it (or close variants), have been around at least since the first half of the 20th century. The usage of "Usian" is not common.
Use of the word has been practiced and advocated to distinguish U.S. nationals from people living in other countries in the Americas. The concern that motivates use of the word is that, since "America" is part of the names of both North America and South America, it follows that "American" means, or ought to be understood to mean, "inhabitant of the Americas".
Other words that have been suggested for the same purpose are Columbian, Columbard, Fredonian, Frede, Unisian, United Statesian, Colonican, Appalacian, Usian, Washingtonian, Usonian (among whose users was Frank Lloyd Wright), Uessian, U-S-ian, and Uesican (in approximately historical order from 1789 to 1939, according to Merriam Webster's Dictionary of English Usage).
Other examples observed in the field:
Links and references: