Positive quadrature formulas on an arc of the unit circle

We analyze positive quadrature formulas associated with Geronimus measures supported on an arc of the unit circle that exactly integrate certain subspaces of Laurent polynomials with the highest possible dimension. The quasi-paraorthogonal polynomials associated with these measures will play a fundamental role in the case of quadrature rules with one node (Szegő-Radau) or two nodes (Szegő-Lobatto) preselected at the end points of the arc.