This paper mainly investigated Noether symmetry and conserved quantity of nonholonomic controllable mechanical systems in phase space on time scales. The Hamilton equation for nonholonomic controllable mechanical systems on the time scale is established. We offered the definitions and criteria of the generalized Noether quasi-symmetry

and conserved quantities deduced from the generalized Noether quasi-symmetry are obtained. In the end of the paper

an example is given to illustrate the application of the results.