Family
John was the son of Saint Stephen the Blind, Despot of Serbia (born 1417, blinded in 1441 by order of the Ottoman Sultan Murad II, died 1476), and of Saint Angelina, daughter of the Albanian prince George Arianiti, whom Stephen married in 1460. His elder brother George (Đorđe) Branković took monastic vows under the name Maximus.
John married Jelena Jakšić, a Serbian noblewoman. By the account in Wikipedia they had four daughters and no surviving male heir; one daughter, Jelena, married Prince Peter IV Rareş of Moldavia. The whole family — Stephen, Angelina, George (Maximus), and John — is venerated together as a holy household of the Branković dynasty.
Exile and rule
The Branković family lived much of its life in exile after the collapse of the medieval Serbian state under Ottoman pressure. Wikipedia records that Emperor Friedrich III granted the family Castle Weitensfeld in Carinthia in 1479. By John's lifetime the title of Despot of Serbia, which he bore, had become largely titular rather than the rule of an independent state.
After John's death his widow Jelena remarried Ivaniš Berislavić, who was in turn granted the title Despot of Serbia.
Relics and Veneration
John was buried at the Monastery of Krušedol (Krushedol) in Fruška Gora, the monastery associated with his brother Maximus and with the burials of his family. The synaxarion relates that many miracles took place before his holy relics.
John was proclaimed a saint by the Serbian Orthodox Church; according to Wikipedia his cult began in the first half of the 16th century. He is commemorated together with his parents, Saint Stephen and Saint Angelina, on December 10.