Apple Music

genre based radio Station? Yes. You can.

genre based songs on iPhone? No.

Listen to streaming radio from Beats 1, NPR, and other live stations4 in this tab. If you subscribe to Apple Music, you can also listen to genre-based radio stations or create your own. Learn more about Radio in Apple Music.

https://support.apple.com/en-us/HT204951#listen

Best option is to type the genre you're looking for into the search section. A wealth of playlists, songs and radio stations should appear for whatever genre you're after.