<p>On-device session-based recommendation has emerged as a key paradigm for delivering efficient services under limited computational resources. To adapt to resource-constrained devices, existing solutions typically introduce auxiliary information or employ model compression and pruning techniques. However, when faced with highly sparse data scenarios, these methods often struggle to strike an optimal balance between representation capacity and model compactness. To this end, we propose MKDRec, a Multi-source Knowledge Distillation Framework by mitigating data sparsity for on-device recommendation. Specifically, we first leverage a Large Language Model (LLM) to fuse multi-source sparse data, constructing context-rich dense semantic representations. Then, we design an Informer-based architecture that integrates the ProbSparse attention with Mixture-of-Experts feed-forward layers. Finally, we formulate Wasserstein distance-based knowledge distillation to achieve geometric alignment under sparse distributions. Extensive experimental results on two benchmark datasets demonstrate that this framework significantly outperforms existing state-of-the-art methods in terms of recommendation performance.</p>