If the supplication is made before the Tashahhud, it invalidates the prayer; because it is a request similar to what people ask for, and that invalidates the prayer. However, after the Tashahhud, it does not invalidate it; because the essence of people's speech after the Tashahhud does not invalidate the prayer, so how can anything resembling it do so. See: Al-‘Inayah 1: 277.