This page of the Spider-Man Miles Morales guide clarifies whether J.Jonah Jameson appears in the game.
John Jonah Jameson is a side character from Marvel's Spider-Man series. The former publisher of the Daily Bugle newspaper hosts a radio show "Just the Facts", wherein he notoriously denigrates Spider-Man.
During the first main mission, after Rhino accidentally bursts through the set of the podcast, we can see Jameson dressed as Santa Claus for a brief moment. He shouts at Spider-Man, calling him various names. When Pete leaves New York, Jameson continues the podcast series and makes Miles the new target for his slander. JJJ constantly comments on recently completed main and side missions, as well as activities from the FNSM app.
Archival episodes of Jameson's podcast can be found in the Collections tab after pressing the touchpad. These podcasts are collected automatically when you travel around town. Please note that the order of the episodes may vary.