This paper identifies vulnerabilities in model fingerprinting techniques for protecting the intellectual property rights of open-source models and proposes a novel approach to address them. We demonstrate that existing fingerprinting techniques, due to their untargeted comparison method, are vulnerable to false claim attacks, where attackers falsely claim a model as their own. Therefore, we propose FIT-Print, a targeted fingerprinting paradigm, and develop two black-box model fingerprinting techniques, FIT-ModelDiff and FIT-LIME, which utilize the distance between model outputs and the feature importance of specific samples. Experimental results demonstrate that the proposed method is more robust and effective against false claim attacks than existing methods.