Defects and impurities within semiconductor materials pose significant challenges. This investigation scrutinizes the response of a single dopant donor impurity located in nanostructured semiconductors, specifically quantum wells subjected to both harmonic and inharmonic confinement potentials. The primary focus of this inquiry centers on the analysis of binding energy, electron probability distribution, and diamagnetic susceptibility in connection with both the ground (1s) and excited (2p) electron states. Utilizing advanced computational techniques, specifically the Finite Elements Method (FEM) implemented through Python code, this study unveils a marked alteration in the interaction between electrons and impurities when exposed to external fields. Significantly, the characteristics of the confinement potential exert a substantial influence on the explored physical parameters. This research significantly advances our understanding of the interaction between impurities and intense fields, offering valuable insights into solid-state phenomena within low-dimensional systems. Consequently, it contributes to the design and fabrication of next-generation applications in the field of quantum well systems, encompassing areas such as lighting, detection, information processing, sensing, and energy conversion.