  Geyer and Jarden proved several results for torsion points of elliptic curves
defined over the fixed field by finitely many elements in the absolute Galois
group of a finitely generated field over the prime field in its algebraic
closure. As an analogue of these results, this paper studies torsion points of
Drinfeld modules defined over the fixed field by finitely many elements in the
absolute Galois group of a finitely generated function field in its algebraic
closure. We prove some results which are similar to those of Geyer and Jarden.
