One month in paediatry, off and on (4)
I believe the answer is:
adar
'one month' is the definition.
(Adar is an example)
'paediatry off and on' is the wordplay.
'off and on' indicates alternate letters (letters taken on and off, on a regular basis).
The alternate letters of 'paediatry' are 'ADAR'.
'in' acts as a link.
(Other definitions for adar that I've seen before include "Jewish month" , "period for Jewish people" , "month in Israel?" .)