Mysterious notice inscribed with second digital symbol (8)
I believe the answer is:
emoticon
'digital symbol' is the definition.
(symbol used in digital communication)
'mysterious notice inscribed with second' is the wordplay.
'mysterious' indicates anagramming the letters.
'inscribed with' indicates putting letters inside (I've seen this in other clues).
'second' becomes 'mo' (both are short periods of time).
'notice' is an anagram of 'eticon'.
'eticon' going around 'mo' is 'EMOTICON'.
(Other definitions for emoticon that I've seen before include "Smiley, eg" , "symbol of modern communication" , "Moody characters" , "Graphic way of conveying feeling in e-mails" , "Wordless expression" .)