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The spectral landscape and the transport property of a translationally invariant network with side-coupled quantum dots are demonstrated within the tight-binding framework. For periodic environment band structure is demonstrated analytically in details. Moreover, if the side-coupling here follows a typical quasiperiodic Aubry-Andre-Harper type of modulation then such off-diagonal disorder invites an exotic spectral feature for this model quantum system. We perform an in-depth numerical analysis followed by the evaluation of the density of eigenstates and the inverse participation ratio. The description shows that this network creates a typical self-similar kind of multifractal pattern in the energy landscape. The impacts of the strength of such aperiodic connectivity and the slowness parameter are reported in this analysis. In the present era of advanced technology and lithography techniques all such non-trivial results definitely throw an achievable challenge to the experimentalists to study the localization of excitation in such network, 5 pages (brief communication as conference publication), Proceedings of International Conference on Recent Trends in Physics and Allied Sciences, Vol. No. 1, Page-73-77 (2023), ISBN-978-93-89817-84-3

Controlled Aharonov-Bohm caging of wave train is reported in a quasi-one dimensional version of Lieb geometry with next nearest neighbor hopping integral within the tight-binding framework. This longer wavelength fluctuation is considered by incorporating periodic, quasi-periodic or fractal kind of geometry inside the skeleton of the original network. This invites exotic eigenspectrum displaying a distribution of flat band states. Also a subtle modulation of external magnetic flux leads to a comprehensive control over those non-resonant modes. Real space renormalization group method provides us an exact analytical prescription for the study of such tunable imprisonment of excitation. The non-trivial tunability of external agent is important as well as challenging in the context of experimental perspective., Comment: 11 pages, 25 eps figures