  Let $K$ be a number field. Let $S$ be a finite set of places of $K$
containing all the archimedean ones. Let $R_S$ be the ring of $S$-integers of
$K$. In the present paper we consider endomorphisms of $\pro$ of degree 2,
defined over $K$, with good reduction outside $S$. We prove that there exist
only finitely many such endomorphisms, up to conjugation by ${\rm PGL}_2(R_S)$,
admitting a periodic point in $\po$ of order $>3$. Also, all but finitely many
classes with a periodic point in $\po$ of order 3 are parametrized by an
irreducible curve.
