By the 1920s, most of the earliest animated studios had closed, leaving Fleischer and Terry (whom we'll get to later), joined by Pat Sullivan. According to Leonard Maltin's Of Mice and Magic (the inspiration and source for this series of posts), Sullivan was born in Australia and eventually made his way to America where he took over William F. Marriner's comic strips after Marriner died (Sullivan was working as Marriner's assistant). Sullivan's first animated film was based on one of these strips, and the series was called Sammie (or Sammy) Johnsin, starting in 1916. Sullivan worked with Otto Messmer, and Messmer's contributions soon outweighed Sullivan's (although Sullivan would continue to take credit for the cartoons even after he barely had anything to do with them).
Sullivan's next series was some Charlie Chaplin cartoons, followed by the Boomer Bill series, but Malton says that Messmer was most proud of "20,000 Laughs Under the Sea," a parody of the Universal feature version of Jules Verne's novel. In 1919, after John R. Bray left Paramount to release his films through MGM, Paramount went to Paul Terry and Pat Sullivan to contribute cartoons for their Paramount Screen Magazine. Messmer created the first of these, featuring a black cat that would become known as Felix, and the first of this series, released in 1919, is Feline Follies!
If you're only familiar with Felix through the TV cartoons, you'll note that he's quite a different cat in these cartoons! Felix wasn't officially named until the second installment, "Musical Mews." At the end of 1921, Sullivan left Paramount to branch out on his own, with Felix cartoons coming out on a monthly basis, beginning with "Felix Saves the Day," released in 1922, and made almost entirely by Messmer.