It depends on what you consider a "sequel."
The Broadway Melody of 1936, nominated for Best Picture of 1935, was a continuation
of MGM's successful series that began with 1929's Best Picture The Broadway Melody and
would include additional installments in 1938 and 1940.
But aside from the title and the backstage
setting, the films had little connection to each other, having completely different characters and stories.
Beginning in 1936, at least the casting gained some uniformity (Eleanor Powell starred in the final
three installments, and Robert Taylor, Buddy Ebsen and George Murphy each appeared in two), but
the actors played different characters in all the films (none of the cast of the 1929 version appeared
of the later installments).
A more literal sequel was 1945's Best Picture nominated
The Bells of St. Mary's starring
Bing Crosby and Ingrid Bergman and directed by
Leo McCarey. It continued the story of Father Chuck O'Malley, Crosby's character from
previous year's Best Picture, Going My Way. While shooting the
sequel, Crosby and
McCarey won the Oscars for Best Actor and Director, and Bergman won the
Best Actress Award for Gaslight. When she accepted the trophy,
she said "I'm
so glad I won. I was afraid if I showed up on the set without an Oscar
Bing and Mr. McCarey wouldn't speak to me."
Most references answer this question with The Bells of St. Mary's but if
you said The Broadway Melody of 1936, you obviously know your stuff.
Full credit for either answer.