  We prove every oriented compact cyclic $3$-orbifold has a contact structure.
There is another proof in the web by Daniel Herr in his uploaded thesis which
depends on open book decompositions, ours is independent of that. We define
overtwisted contact structures, tight contact structures and Lutz twist on
oriented compact cyclic 3-orbifolds. We show every contact structure in an
oriented compact cyclic $3$-orbifold contactified by our method is homotopic to
an overtwisted structure with the overtwisted disc intersecting the singular
locus of the orbifold. We pose Eliashberg's like characterization of
overtwisted contact structures of cyclic $3$-orbifolds as an open problem. In
course of proving the above results we prove a classification result for
compact oriented cyclic-3 orbifolds which has not been seen by us in literature
before.
