。
I went there on an errand for my father.
Literal
I [topic-は] father [attributive-の] errand [on-で] there [to-に] went.
使い ('errand, messenger,' a noun from 使う 'use/employ'). The phrase ~の使いで ('on someone's errand') is a set expression. で here marks the purpose/capacity. Common in contexts where children are sent on errands, with a slight old-fashioned feel.