As Richard said, the key signature goes after the barline, but strictly speaking the "start repeat" mark is not a barline! For example, start and end repeat marks often occur in the middle of a bar, without interrupting the rhythm of the music.
At the start of a system, there is no barline between the key signature and the first note or rest, but there may be a "start repeat" mark in that position.
You will never see the key signature after the start repeat at the start of a system. Usually, there will be a "cautionary" key signature after the last barline in the previous system - i.e. right at the end of the previous system.
In the middle of a system, the correct notation is this:
However there are published scores which (incorrectly, by the modern "rules") omit the "double bar" at the key change, and put the key signature after the "start repeat" sign.
If the music before the key change is also repeated, the key signature goes between the "end repeat" and "start repeat" lines: