Deep learning methods have significantly advanced medical image segmentation, yet their success hinges on large volumes of manually annotated data, which require specialized expertise for accurate labeling. Additionally, these methods often demand substantial computational resources, particularly for three-dimensional medical imaging tasks. Consequently, applying deep learning techniques for medical image segmentation with limited annotated data and computational resources remains a critical challenge. In this paper, we propose a novel parameter-efficient fine-tuning strategy, termed HyPS, which employs a hybrid parallel and serial architecture. HyPS updates a minimal subset of model parameters, thereby retaining the pre-trained model's original knowledge tructure while enhancing its ability to learn specific features relevant to downstream tasks. We apply this strategy to the state-of-the-art SwinUNETR model for medical image segmentation. Initially, the model is pre-trained on the BraTs2021 dataset, after which the HyPS method is employed to transfer it to three distinct hippocampus datasets.Extensive experiments demonstrate that HyPS outperforms baseline methods, especially in scenarios with limited training samples. Furthermore, based on the segmentation results, we calculated the hippocampal volumes of subjects from the ADNI dataset and combined these with metadata to classify disease types. In distinguishing Alzheimer's disease (AD) from cognitively normal (CN) individuals, as well as early mild cognitive impairment (EMCI) from late mild cognitive impairment (LMCI), HyPS achieved classification accuracies of 83.78% and 64.29%, respectively. These findings indicate that the HyPS method not only facilitates effective hippocampal segmentation using pre-trained models but also holds potential for aiding Alzheimer's disease detection. Our code is publicly available.