Large foundation models (FMs) adapt surprisingly well to specific domains or tasks with fine-tuning. Federated learning (FL) further enables private FM fine-tuning using the local data on devices. However, the standard FMs' large size poses challenges for resource-constrained and heterogeneous devices. To address this, we consider FMs with reduced parameter sizes, referred to as on-device FMs (ODFMs). While ODFMs allow on-device inference, computational constraints still hinder efficient federated fine-tuning. We propose a parameter-efficient federated fine-tuning method for ODFMs using heterogeneous low-rank approximations (LoRAs) that addresses system and data heterogeneity. We show that homogeneous LoRA ranks face a trade-off between overfitting and slow convergence, and propose HetLoRA, which employs heterogeneous ranks across clients and eliminates the shortcomings of homogeneous HetLoRA. By applying rank self-pruning locally and sparsity-weighted aggregation at the server, we combine the advantages of high and low-rank LoRAs, which achieves improved convergence speed and final performance compared to homogeneous LoRA. Furthermore, it offers enhanced computation efficiency compared to full fine-tuning, making it suitable for heterogeneous devices while preserving data privacy.