There are no other characters who we know of that started and finished school in the same year as Tom Riddle. However we do know of some students who attended at some point while he did.
Known students who were in Hogwarts during 1938 - 1945:
Chat with our AI personalities
1937
La vierge folle - 1938 was released on: France: 24 November 1938 USA: 29 December 1938 Portugal: 18 March 1939
Land of Fighting Men - 1938 was released on: USA: 11 March 1938 Portugal: 12 June 1944
Uncle Si and the Sirens - 1938 was released on: USA: 1938
Allama Iqbal emerged from the following dates 1877-1938.