The identification of Alzheimer's disease (AD) using structural magnetic resonance imaging (sMRI) has been studied based on the subtle morphological changes in the brain. One of the typical approaches is a deep learning-based patch-level feature representation. For this approach, however, the predetermined patches before learning the diagnostic model can limit classification performance. To mitigate this problem, we propose the BrainBagNet with a position-based gate (PG), which applies position information of brain images represented through the 3D coordinates. Our proposed method represents the patch-level class evidence based on both MR scan and position information for image-level prediction. To validate the effectiveness of our proposed framework, we conducted comprehensive experiments comparing it with state-of-the-art methods, utilizing two publicly available datasets: the Alzheimer's Disease Neuroimaging Initiative (ADNI) and the Australian Imaging, Biomarkers and Lifestyle (AIBL) dataset. Furthermore, our experimental results demonstrate that our proposed method outperforms the existing competing methods in terms of classification performance for both AD diagnosis and mild cognitive impairment conversion prediction tasks. In addition, we performed various analyses of the results from diverse perspectives to obtain further insights into the underlying mechanisms and strengths of our proposed framework. Based on the results of our experiments, we demonstrate that our proposed framework has the potential to advance deep-learning-based patch-level feature representation studies for AD diagnosis and MCI conversion prediction. In addition, our method provides valuable insights, such as interpretability, and the ability to capture subtle changes, into the underlying pathological processes of AD and MCI, benefiting both researchers and clinicians.