Federated learning (FL) is one of the most widely used distributed machine learning frameworks. However, FL is susceptible to poisoning attacks that can degrade the quality of the global model. Recent studies on fine-grained poisoning attacks highlight a strategic shift where attackers no longer prioritize maximal disruption of the global model, but instead control the degree of model poisoning to maintain stealth and avoid detection. However, research on fine-grained poisoning is still in the infant stage. Numerous fundamental questions have yet to be addressed, including its underlying mechanisms and optimization strategies. To this end, we introduces FGP, the first comprehensive framework for Fine-Grained Poisoning on FL, which allows adversaries to precisely manipulate the global model by strategically inducing accurate and stealthy sub-optimal solution. Fundamentally, FGP innovatively formalizes fine-grained attacks as an optimization problem to minimize the distance between the current global model and the adversary's target (a sub-optimal solution). It then employs a real-time search strategy to dynamically refine the malicious model updates in each round. To ensure optimal attack performance, we further introduce a novel topology-based approach as the error feedback. Additionally, we present a formal convergence analysis of our attacks. Armed with FGP, we conduct a comprehensive evaluation of FL's robustness against fine-grained poisoning across diverse settings. Results demonstrate that FGP significantly outperforms the prior work, achieving an average 6.5x higher attack accuracy.