Early screening for Alzheimer's Disease (AD) through speech presents a promising non-invasive approach. However, challenges such as limited data and the lack of fine-grained, adaptive feature selection often hinder performance. To address these issues, we propose MoTAS, a robust framework designed to enhance AD screening efficiency. MoTAS leverages Text-to-Speech (TTS) augmentation to increase data volume and employs a Mixture of Experts (MoE) mechanism to improve multimodal feature selection, jointly enhancing model generalization. The process begins with automatic speech recognition (ASR) to obtain accurate transcriptions. TTS is then used to synthesize speech that enriches the dataset. After extracting acoustic and text embeddings, the MoE mechanism dynamically selects the most informative features, optimizing feature fusion for improved classification. Evaluated on the ADReSSo dataset, MoTAS achieves a leading accuracy of 85.71\%, outperforming existing baselines. Ablation studies further validate the individual contributions of TTS augmentation and MoE in boosting classification performance. These findings highlight the practical value of MoTAS in real-world AD screening scenarios, particularly in data-limited settings.