Answer is C imo.
A. played on one of the most influential jazz albums ever and with some of the art’s greatest performers, considered by critics to be a turning point in recorded jazz --> Here "considered" is modifying the action of playing, which is incorrect. Considered is a modifier which should modify a noun.
B. considered by critics to be a turning point in recorded jazz, played on many of the most influential jazz albums and with some of the art’s greatest performers --> A person cannot be a turning point, so this is incorrect.
C. played on one of the most influential jazz albums ever, considered by critics to be a turning point in recorded jazz, and with some of the art’s greatest performers --> considered correctly modifies album.
D. played on one of the most influential jazz albums, considered as a turning point in recorded jazz by critics and with some of the art’s greatest performers -->there should be a comma after critics. Incorrect structure.
E. played, considered by critics to be a turning point in recorded jazz, on one of the most influential jazz albums ever, and with some of the art’s greatest performers. -->Here "considered by..." is modifying "played" which is a verb and so it's incorrect.