  We define successive minimal bases (SMBs) for the space of $u^{n}$-division
points of a Drinfeld $\mathbb{F}_{q}[t]$-module over a local field, where $u$
is a finite prime of $\mathbb{F}_{q}[t]$ and $n$ is a positive integer. These
SMBs share similar properties to those of SMBs of the lattices associated to
Drinfeld modules. We study the relations between these SMBs and those of the
lattices. Finally, we apply the relations to study the explicit wild
ramification subgroup action on an SMB of the space of $u^{n}$-division points
and show the function field analogue of Szpiro's conjecture for rank $2$
Drinfeld modules under a certain limited situation.
