The Roffignac cocktail was invented in New Orleans at some date before 1874 and was named after Louis Philippe de Roffignac, who was Mayor of New Orleans from 1820 to 1828, not long after Louisiana became a US state. The cocktail remained popular in New Orleans until the 1960s.
From two early sources it appears that the Roffignac was invented around 1870 and may have been named to suggest rivalry with the Sazerac cocktail. The Sazerac coffee house was already popular and served spirits mixed with bitters, although it is not certain that its signature cocktail had been named at this early date.
The earliest source is an advertisement printed in the New Orleans Bulletin (August 2, 1874), which demonstrates that the "Roufignac" was a speciality of Harrison's coffee shop:
Harrison was soon afterwards prosecuted for selling liquor without a licence, which suggests that his "syrups", and naturally his "Roufignac", were fortified with brandy or whiskey.
The second source is a citation of a bartender, T. P. Thompson, in the Washington Post (January 9, 1911). It includes the false claims that the "Roupegnac" was first mixed by the very mayor of New Orleans after whom it was named, and that the Sazerac was invented by a man named Sazerac, but it shows that the two cocktails were seen as rivals:
After Harrison's time the Roffignac became a popular drink at Mannessier's confectionery in the late 19th century, and was later the signature cocktail of Maylié's creole restaurant, which survived until 1969.