Dictionary.net

At the suit of. Commonly abbreviated to ads. Used in entering and indexing the names of cases, where it is desired that the name of the defendant should come first. Thus, "B. ads. A." indicates that B. is defendant in an action brought by A., and the title so written would be an inversion of the more usual form "A. v. B."

At the suit of, commonly abbreviated ads. It isusual in filing pleas, and other papers, for a defendant, instead of putting the name of the plaintiff first, as Peter v. Paul to put his own first, and instead of v. to put ads., as Paul ads. Peter.