Large language models (LLMs) are revolutionizing how we interact with information, but they still face challenges when tackling complex tasks like named entity recognition (NER) in scientific literature. Imagine trying to find specific materials, genes, or diseases mentioned in a massive pile of research papers—it's like finding a needle in a haystack. LLMs can help automate this process, but their accuracy depends heavily on the examples they learn from. If the examples aren't representative of the overall data, the LLM can get confused, leading to errors. Researchers have been exploring different ways to select these examples, using either a static approach where the same examples are used for all texts, or a dynamic approach where examples are chosen based on their similarity to the text being analyzed. A new hybrid method called STAYKATE combines the best of both worlds. It uses a clever technique called representativeness sampling to select static examples that cover the diverse patterns in scientific text, and combines this with a retrieval-based approach to find dynamically relevant examples. Experiments on datasets from materials science, biology, and biomedicine show that STAYKATE significantly improves the accuracy of LLMs in extracting key entities. Especially in cases where entities are domain-specific and require specialized knowledge, STAYKATE helps the LLM understand subtle nuances and avoid common errors like over-prediction. This means that researchers can more easily sift through mountains of scientific papers to find the crucial information they need. While there's still room for improvement, STAYKATE represents a major step forward in making LLMs more reliable and effective for scientific information extraction.