Mean things periodically atop empty shed (5)
I believe the answer is:
tight
'mean' is the definition.
(both can mean miserly)
'things periodically atop empty shed' is the wordplay.
'periodically' indicates alternate letters (letters must be selected 'every so often').
'atop empty shed' becomes 'ht' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
The alternate letters of 'things' are 'tig'.
'tig'+'ht'='TIGHT'
Can you help me to learn more?
(Other definitions for tight that I've seen before include "with limited room to manoeuvre" , "Close-fitting; drunk" , "Drunk - under control" , "corked?" , "Tense; secretive" .)