If you define a “subway series” as a World Series in which the American League and National teams both represent the same city, then the 1906 series which pitted the Cubs against the White Sox certainly meets that definition. However while parts of the “L” had already been constructed in 1906, the trains didn’t start running underground there until 1943.
1906 was the one and only time when Cubs and White Sox played each other in the World Series. Subway series? Your call.
In 1921 and 1922 the Yankees played the New York Giants in the World Series. By that time the subway system was an integral part of New York life. But to call either of those World Series a “subway series” is a bit of stretch, since all of the games were played at the Polo Grounds.
In 1923 the Yanks and the Giants squared off in the Fall Classic for the third straight time, but this time, but this time the series moved back and forth between the brand new Yankee Stadium in the Bronx, and the Polo Grounds in upper Manhattan. Therefore, if you define a subway series as one where you can take the subway from one team’s ballpark to the other’s, then you would be correct to say that the first subway series was played in 1923. After 1923 The Yankees and the Giants played in three more subway series (1936, 1937 and 1951.)
The Yankees and the Brooklyn Dodgers also played in six subway series (1941, 1947, 1952, 1953, 1955 and 1956.)
The most recent subway series was played in 2000, between the Yankees and the Mets.
In 1944 St. Louis hosted what was called “The Trolley Series” (St. Louis has never had a subway system.) when the Cardinals and the St. Louis Browns faced off in the World Series. As was the case in the first two Yankees-Giants series, all of the games of the 1944 World Series were played at Sportsman’s Park.