The local team scored three goals . . . . . . . . the first half of the match.

The correct sentence is:

The local team scored three goals in the first half of the match.

The preposition "in" is used to indicate a specific period of time during which something happens.

In this context, it refers to the duration of the first half of the match when the goals were scored.

Using "in" correctly links the action of scoring goals to the specific time frame of the first half.