  Motivated by some previous works of Rudra et al we set to explore the
background dynamics when dark energy in the form of New Variable Modified
Chaplygin gas is coupled to dark matter with a suitable interaction in the
universe described by brane cosmology. The main idea is to find out the
efficiency of New variable modified Chaplygin gas to play the role of DE. As a
result we resort to the technique of comparison with standard dark energy
models. Here the RSII brane model have been considered as the gravity theory.
An interacting model is considered in order to search for a possible solution
of the cosmic coincidence problem. A dynamical system analysis is performed
because of the high complexity of the system . The statefinder parameters are
also calculated to classify the dark energy model. Graphs and phase diagrams
are drawn to study the variations of these parameters and get an insight into
the effectiveness of the dark energy model. It is also seen that the background
dynamics of New Variable Modified Chaplygin gas is consistent with the late
cosmic acceleration. After performing an extensive mathematical analysis, we
are able to constrain the parameters of new variable modified Chaplygin gas as
$m<n$ to produce the best possible results. Future singularities are studied
and it is found that the model has a tendency to result in such singularities
unlike the case of generalized cosmic Chaplygin gas. Our investigation leads us
to the fact that New Variable Modified Chaplygin gas is not as effective as
other Chaplygin gas models to play the role of dark energy.
