  We investigate the spectral and transport properties of a two-arm
tight-binding ladder perturbed by an external magnetic field following an
Aubry-Andr\'e-Harper profile. The varying magnetic flux trapped in consecutive
ladder-cells simulates an axial twist that enables us, in principle, to probe a
wide variety of systems ranging from a ribbon Hofstadter geometry to helical
DNA chains. We perform an in-depth numerical analysis, using a direct
diagonalization of the lattice Hamiltonian to study the electronic spectra and
transport properties of the model. We show that such a geometry creates a
self-similar multifractal pattern in the energy landscape. The spectral
properties are analyzed using the local density of states and a Green's
function formalism is employed to obtain the two-terminal transmission
probability. With the standard multifractal analysis and the evaluation of
inverse participation ratio we show that, the system hosts both critical and
extended phase for a slowly varying aperiodic sequence of flux indicating a
possible mobility edge. Finally, we report signatures of topological edge modes
that are found to be robust against a correlated perturbation given to the
nearest neighbor hopping integrals. Our results can be of importance in
experiments involving ladder-like quantum networks, realized with cold atoms in
an optical trap setup.
