When one thinks of the term "Trumpet Jazz", one invariably thinks of Miles Davis, in my opinion the uncontested "Father of Trumpet Jazz".
"Miles Dewey Davis III (May 26, 1926 – September 28, 1991) was an American jazz trumpeter, bandleader, and composer. He is among the most influential and acclaimed figures in the history of jazz and 20th century music. Davis adopted a variety of musical directions in a five-decade career that kept him at the forefront of many major stylistic developments in jazz." –Wikipedia
Miles was born and raised in Illinois but studied at Julliard in New York and came onto the Jazz scene as the trumpeter in Charlie Parker's group. He went on to record for Capital Records, laying down some of the earliest Bebop music on Prestige records while battling a heroin addiction.