Physical-Layer Authentication (PLA) has been recently believed as an endogenous-secure and energy-efficient technique to recognize IoT terminals. However, the major challenge of applying the state-of-the-art PLA schemes directly to 6G-enabled IoT is the inaccurate channel fingerprint estimation in low Signal-Noise Ratio (SNR) environments, which will greatly influence the reliability and robustness of PLA. To tackle this issue, we propose a configurable-fingerprint-based PLA architecture through Intelligent Reflecting Surface (IRS) that helps create an alternative wireless transmission path to provide more accurate fingerprints. According to Baye's theorem, we propose a Gaussian Process Classification (GPC)-based PLA scheme, which utilizes the Expectation Propagation (EP) method to obtain the identities of unknown fingerprints. Considering that obtaining sufficient labeled fingerprint samples to train the GPC-based authentication model is challenging for future 6G systems, we further extend the GPC-based PLA to the Efficient-GPC (EGPC)-based PLA through active learning, which requires fewer labeled fingerprints and is more feasible. We also propose three fingerprint selecting algorithms to choose fingerprints, whose identities are queried to the upper-layers authentication mechanisms. For this reason, the proposed EGPC-based scheme is also a lightweight cross-layer authentication method to offer a superior security level. The simulations conducted on synthetic datasets demonstrate that the IRS-assisted scheme reduces the authentication error rate by 98.69% compared to the non-IRS-based scheme. Additionally, the proposed fingerprint selection algorithms reduce the authentication error rate by 65.96% to 86.93% and 45.45% to 70.00% under perfect and imperfect channel estimation conditions, respectively, when compared with baseline algorithms.