The battle to replace the country’s longest-serving Hispanic congressman could show the strength of ethnic voting blocs in one of the country’s few majority-Latino districts.

Democrats started jockeying immediately when U.S. Rep. Jose Serrano announced in March that he wouldn’t run again to represent the 15th District in the Bronx. Mr. Serrano is battling Parkinson’s disease. He was first elected to Congress in 1990.

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