Cloud-edge-end systems offer a promising framework for real-time, privacy-conscious hand gesture recognition, driving considerable research in multimodal sensing. Manually-designed multimodal deep networks for multimodal hand gesture recognition (MHGR) typically necessitate substantial domain expertise and laborious manual adjustment. To address these limitations, we propose an evolutionary network architecture search framework featuring adaptive multimodal fusion (AMF-ENAS), which automates the design of multimodal deep networks. Our framework incorporates a novel multimodal fusion strategy that co-optimizes the locations of fusion nodes and the fusion ratios across distinct network branches. This strategy effectively captures feature representations at both shallow and deep layers while accounting for the differential importance of various modalities. Moreover, we introduce an encoding strategy for multimodal data adaptation, organizing the search space into three key components: fusion locations, fusion ratios, and block selection. This encoding facilitates flexible architecture customization, allowing the evolutionary algorithm to iteratively seek optimal configurations for diverse multimodal datasets. Experimental results demonstrate that AMF-ENAS achieves average MHGR accuracies of 95.15%, 92.50%, and 97.19% on the benchmark datasets Ninapro DB2, DB3, and DB7, respectively, surpassing the performance of existing multimodal deep neural networks.