  Periodic surface homemorphisms (diffeomorphisms) play a significant role in
the the Nielsen-Thurston classification of surface homeomorphisms. Periodic
surface homeomorphisms can be described (up to conjugacy) by using data sets
which are combinatorial objects. In this article, we start by associating a
rational open book to a slight modification of a given data set, called marked
data set. It is known that every rational open book supports a contact
structure. Thus, we can associate a contact structure to a periodic map and
study the properties of it in terms combinatorial conditions on marked data
sets.
  In particular, we prove that a class of data sets, satisfying easy-to-check
combinatorial hypothesis, gives rise to Stein fillable contact structures. In
addition to the above, we prove an analogue of Mori's construction of explicit
symplectic filling for rational open books. We also prove a sufficient
condition for Stein fillability of rational open books analogous to the
positivity of monodromy in honest open books as in the result of Giroux and
Loi-Piergallini.
