Q. When is surah kahf read? Friday morning or after 12 at night Thursday night?
A: It can be read from Thursday after sunset to Friday before sunset.
Allah Certainly Knows Best.
p.s. If Allah has blessed you with the ability to recite this surah, you should most certainly try and recite it.
(one can also read it everyday, the reward for this too would be great. It would save you inshallAllah form the agents and fitnah of dajjal.)