  We prove that closed surfaces of all topological types, except for the
non-orientable odd-genus ones, can be minimally embedded in the Riemannian
product of a sphere and a circle of arbitrary radius. We illustrate it by
obtaining some periodic minimal surfaces in $\mathbb{S}^2\times\mathbb{R}$ via
conjugate constructions. The resulting surfaces can be seen as the analogy to
the Schwarz P-surface in these homogeneous 3-manifolds.
