In the Fourth Industrial Revolution, wherein artificial intelligence and the automation of machines occupy a central role, the deployment of robots is indispensable. However, the manufacturing process using robots, especially in collaboration with humans, is highly intricate. In particular, modeling the friction torque in robotic joints is a longstanding problem due to the lack of a good mathematical description. This motivates the usage of data-driven methods in recent works. However, model-based and data-driven models often exhibit limitations in their ability to generalize beyond the specific dynamics they were trained on, as we demonstrate in this paper. To address this challenge, we introduce a novel approach based on residual learning, which aims to adapt an existing friction model to new dynamics using as little data as possible. We validate our approach by training a base neural network on a symmetric friction data set to learn an accurate relation between the velocity and the friction torque. Subsequently, to adapt to more complex asymmetric settings, we train a second network on a small dataset, focusing on predicting the residual of the initial network's output. By combining the output of both networks in a suitable manner, our proposed estimator outperforms the conventional model-based approach, an extended LuGre model, and the base neural network significantly. Furthermore, we evaluate our method on trajectories involving external loads and still observe a substantial improvement, approximately 60-70%, over the conventional approach. Our method does not rely on data with external load during training, eliminating the need for external torque sensors. This demonstrates the generalization capability of our approach, even with a small amount of data--less than a minute--enabling adaptation to diverse scenarios based on prior knowledge about friction in different settings.