  In this paper, we study {\bf twisted Milnor hypersurfaces} and compute their
$\hat A$-genus and Atiyah-Singer-Milnor $\alpha$-invariant. Our tool to compute
the $\alpha$-invariant is Zhang's analytic Rokhlin congruence formula. We also
give some applications about group actions and metrics of positive scalar
curvature on twisted Milnor hypersurfaces.
