Your question is addressed in the following paper:

The twin paradox in compact spaces
Authors: John D. Barrow, Janna Levin
Phys.Rev. A63 (2001) 044104

Abstract: Twins travelling at constant relative velocity will each see the other's time dilate leading to the apparent paradox that each twin believes the other ages more slowly. In a finite space, the twins can both be on inertial, periodic orbits so that they have the opportunity to compare their ages when their paths cross. As we show, they will agree on their respective ages and avoid the paradox. The resolution relies on the selection of a preferred frame singled out by the topology of the space.

Your question is addressed in the following paper:

The twin paradox in compact spaces
Authors: John D. Barrow, Janna Levin
Phys. Rev. A 63 no. 4, (2001) 044104
arXiv:gr-qc/0101014

Abstract: Twins travelling at constant relative velocity will each see the other's time dilate leading to the apparent paradox that each twin believes the other ages more slowly. In a finite space, the twins can both be on inertial, periodic orbits so that they have the opportunity to compare their ages when their paths cross. As we show, they will agree on their respective ages and avoid the paradox. The resolution relies on the selection of a preferred frame singled out by the topology of the space.