Amusing periodical by a student (7)
I believe the answer is:
comical
'amusing' is the definition.
(I've seen this before)
'periodical by a student' is the wordplay.
'periodical' becomes 'comic'.
'by' is a charade indicator (letters next to each other).
'student' becomes 'L' (as in L-plates for learner drivers).
'comic'+'a'+'l'='COMICAL'
(Other definitions for comical that I've seen before include "Rich" , "Causing laughter" , "priceless" , "Amusing or droll" , "Humorous" .)