The Radio frequency (RF) fingerprinting technique makes highly secure device authentication possible for future networks by exploiting hardware imperfections introduced during manufacturing. Although this technique has received considerable attention over the past few years, RF fingerprinting still faces great challenges of channel-variation-induced data distribution drifts between the training phase and the test phase. To address this fundamental challenge and support model training and testing at the edge, we propose a federated RF fingerprinting algorithm with a novel strategy called model transfer and adaptation (MTA). The proposed algorithm introduces dense connectivity among convolutional layers into RF fingerprinting to enhance learning accuracy and reduce model complexity. Besides, we implement the proposed algorithm in the context of federated learning, making our algorithm communication efficient and privacy-preserved. To further conquer the data mismatch challenge, we transfer the learned model from one channel condition and adapt it to other channel conditions with only a limited amount of information, leading to highly accurate predictions under environmental drifts. Experimental results on real-world datasets demonstrate that the proposed algorithm is model-agnostic and also signal-irrelevant. Compared with state-of-the-art RF fingerprinting algorithms, our algorithm can improve prediction performance considerably with a performance gain of up to 15\%.