From Smithsonian:
Few of us realize, though, that less than 50 years ago, wings were considered one of the least desirable cuts of the chicken—a throwaway part often cooked into stock—and “buffalo” was just a wooly ungulate that wandered the Plains. Despite the recency of the invention, the event itself is shrouded in mystery. Nevertheless, there is one thing we know for certain: the “buffalo” in the name definitively refers to the city in Western New York. The most authoritative account is by New Yorker writer Calvin Trillin, who investigated the dish’s history in 1980 as he sampled the city’s most well-regarded wing joints. He presented two competing versions of how a stroke of serendipity led Teressa Bellissimo, proprietor of the Anchor Bar, to invent the dish in 1964. Her husband Frank Bellissimo, who founded the bar with Teressa in 1939, told Trillin that the invention involved a mistake—the delivery of chicken wings, instead of necks, which the family typically used when cooking up spaghetti sauce. To avoid wasting the wings, he asked Teressa to concoct a bar appetizer; the result was the wing we know today.
Dominic—Frank and Teressa’s son, who took over management of the restaurant sometime in the ’70s—told a slightly more colorful tale: It was late on a Friday night in 1964, a time when Roman Catholics still confined themselves to fish and vegetables on Fridays…Some regulars had been spending a lot of money, and Dom asked his mother to make something special to pass around gratis at the stroke of midnight. Teressa Bellissimo picked up some chicken wings—parts of a chicken that most people do not consider even good enough to give away to barflies—and the Buffalo chicken wing was born. Both Frank and Dominic agreed on a few other crucial details—that Teressa cut each wing in half to produce a “drumstick” and a “flat,” that she deep-fried them without breading and covered them in a hot sauce, and that she served them with celery (from the house antipasto) and blue cheese salad dressing. They also both reported that they became popular within weeks throughout the city, where they were (and are still) simply called “wings” or “chicken wings.”
More here. (Note: For my brother Bhaisab, who introduced me to, and who enjoyed the wings regularly during his three decades of working nextdoor to Anchor Bar as a cardiac surgeon at Buffalo General Hospital)