This work proposes a novel solution to predict pulsar timing residuals with limited data, addressing the critical challenge of data scarcity across spin-frequency subgroups of millisecond pulsars in PTA datasets. The proposed solution applies a Long Short-Term Memory (LSTM) network optimized using the model-agnostic meta-learning algorithm, enabling rapid adaptation to new frequency domain by fine-tuning the LSTM network with only a few-shot of ground truth timing residuals. Particle swarm optimization algorithm is also used for automatic hyperparameter optimization, leading to improved prediction accuracy. Our solution, evaluated on the second data release of the International Pulsar Timing Array (IPTA), demonstrates robust generalization with accurate predictions in three metrics across high-frequency test frequency domains, while requiring only 10% of the timing residuals from these domains for model fine-tuning. Furthermore, our lightweight structure only costs 16.86 MB CPU memory and 18 milliseconds for single-step residual prediction. All these characteristics make our solution highly suitable for real-world applications, where effective and real-time predictions of pulsar timing residuals are essential-particularly in resource-constrained environments with limited computational power, memory, or energy availability.