Drug discovery and development is a complex and costly process, with a substantial portion of the expense dedicated to characterizing the absorption, distribution, metabolism, excretion, and toxicity (ADMET) properties of new drug candidates. While the advent of deep learning and molecular graph neural networks (GNNs) has significantly enhanced in silico ADMET prediction capabilities, reliably quantifying prediction uncertainty remains a critical challenge. The performance of GNNs is influenced by both the volume and the quality of the data. Hence, determining the reliability and extent of a prediction is as crucial as achieving accurate predictions, especially for out-of-domain (OoD) compounds. This paper introduces a novel GNN model called conformalized fusion regression (CFR). CFR combined a GNN model with a joint mean-quantile regression loss and an ensemble-based conformal prediction (CP) method. Through rigorous evaluation across various ADMET tasks, we demonstrate that our framework provides accurate predictions, reliable probability calibration, and high-quality prediction intervals, outperforming existing uncertainty quantification methods.