As large language models are fine-tuned for increasingly specialized tasks, their performance depends more on which training examples are selected than on how many. Given a large heterogeneous training pool and a small target set specifying the desired capability, targeted data selection aims to find a compact subset that maximizes downstream performance. Existing methods score each candidate independently against the target and select the top-ranked examples, yet this point-wise strategy ignores inter-example interactions: at tight budgets the selected subset is dominated by near-redundant points that waste capacity on overlapping information. We propose Query-based Submodular functions with Gradient-guided Synthesis (QSGS), which formulates targeted selection as a submodular graph cut over a gradient similarity graph. A modular relevance term pulls selected examples toward the target task, while a pairwise dispersion penalty suppresses intra-subset redundancy. The resulting objective balances target relevance and intra-subset redundancy using the same formulation across different selection budgets. Empirically, the benefit of diversity-aware selection becomes increasingly pronounced as the data budget decreases. To further close coverage gaps that no selection from existing data can bridge, we introduce a gradient-guided synthesis step that identifies under-covered target directions via residual subspace analysis and generates synthetic examples to fill them. Experiments on MMLU, BBH, and TydiQA across Llama-2, Llama-3, and Mistral, show that QSGS at a 0.5% budget matches or exceeds full-data performance on Mistral-7B, outperforms the strongest baseline across all benchmarks, and yields increasing gains as the budget shrinks.

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