Topological materials, comprising for instance topological insulators, Dirac and Weyl semimetals, are a recently-discovered class of materials exhibiting exotic electronic band structures that give rise to several unconventional physical phenomena, such giant magnetoresistance, photogalvanic and thermoelectric effects, the violation of classical laws of physics (e.g. the Wiedemann-Franz law and the conservation of chirality) and quantum phenomena. Thanks to their outstanding physical properties, topological materials have the potential to be implemented in novel applications and functionalities in the areas of valleytronics, quantum computing, sensing and catalysis. To date, most of the research activities on topological materials have been primarily devoted to the investigation of bulk single crystals. However, in order to implement topological materials in novel technologies it is of primary importance to understand how and to which extent their properties can be manipulated at the nanoscale. The research activities during the project InNaTo were focused on the topological material system CoSi, a high-order Weyl semimetal, which was recently found to exhibit longest surface Fermi arcs in case of CoSi bulk single crystals. At low dimensionality, owing to the increased surface-to-volume ratio, the topological surface states of CoSi may give rise to unprecedented transport properties. The goal of InNaTo was to investigate the properties of CoSi at low dimensions following two main approaches: CoSi nanoscale thin films prepared by molecular beam epitaxy (MBE) and CoSi micro-scale Hall bars fabricated by focused ion beam (FIB) milling. The experimental results on the magnetotransport properties of CoSi micro-scale Hall bars provide a valuable reference for a comparison with bulk CoSi single crystals and CoSi thin films. In particular, it was found that CoSi micro-scale Hall bars prepared by FIB display a negative longitudinal magnetoresistance, which is possibly manifested as a consequence of the phenomenon of chiral anomaly. Concerning CoSi thin films prepared by MBE method, several unexpected anomalies have been observed in the magnetotransport properties, which are correlated with the strong influence of structural and chemical disorder. Furthermore, an unusual resistivity scaling behavior has been observed in amorphous CoSi thin films, which, contrary to conventional metals, display a decrease in resistivity upon reducing the film thickness down to 2 nm. In conclusion, this action opens the path to explore the complexity and the challenges involved in the prospective exploitation of the topological chiral semimetal CoSi in micro- and nanoscale thin films and devices.