Is the BBC's pre-war live adaptation of Karel Capek's R.U.R., broadcast on February 11, 1938, the first science fiction television show? Originally, I would have thought that the American series Captain Video starting in 1949 was the first, and it may have been the first series. But in doing my research before asking the question, I came up with the BBC broadcast. It was a 35 minute extract from the novel. It's so early that I'm tempted to call it the first, but there might be something even older.
Hard to say with certainty but a number of reputable-seeming sources do say it was the first, for example p. 77 of Popular Television Drama: Critical Perspectives says "The first television science-fiction programme was the B.B.C.'s adaptation of R.U.R.", and p. 308 of Guinness World Records 2011 says "1938: First TV sci-fi aired—an adaptation of R.U.R.".