Specifically for the cornet and in the jazz style 1910-1914/6
I assume you’re looking for musical compositions from those years, not for recordings. The first jazz record wasn’t made until 1917. Here are some songs that became traditional jazz standards, by year of composition:
1910
Chinatown, My Chinatown
Some of These Days
Washington and Lee Swing
1911:
Alexander’s Ragtime Band
1912:
My Melancholy Baby
1913:
Ballin’ the Jack
Memphis Blues
Panama
1914:
St. Louis Blues
That’s A-Plenty
Twelfth Street Rag
Way Down Yonder in New Orleans
1915:
Canadian Capers
Georgia Grind
Jelly Roll Blues
Ragging the Scale
1916:
Bugle Call Rag
I Ain’t Got Nobody
Joe Turner Blues
L’il Liza Jane
Yaaka Hula Hickey Dula