With a user-specified minimum utility threshold (minutil), periodic high-utility pattern mining (PHUPM) aims to identify high-utility patterns that occur periodically in a transaction database. A pattern is deemed periodic if its period aligns with the periodicity constraint set by the user. However, users may not be interested in all periodic high-utility patterns (PHUPs). Moreover, setting minutil in advance is also a challenging issue. To address these issues, our research introduces an algorithm called TPU for extracting the most significant top-k periodic and high-utility patterns that may or may not include negative utility values. This TPU algorithm utilizes positive and negative utility lists (PNUL) and period-estimated utility co-occurrence structure (PEUCS) to store pertinent itemset information. It incorporates the periodic real item utility (PIU), periodic co-occurrence utility descending (PCUD), and periodic real utility (PRU) threshold-raising strategies to elevate the thresholds rapidly. By using the proposed threshold-raising strategies, the runtime was reduced by approximately 5\% on the datasets used in the experiments. Specifically, the runtime was reduced by up to 50\% on the mushroom\_negative and kosarak\_negative datasets, and by up to 10\% on the chess\_negative dataset. Memory consumption was reduced by about 2\%, with the largest reduction of about 30\% observed on the mushroom\_negative dataset. Through extensive experiments, we have demonstrated that our algorithm can accurately and effectively extract the top-k periodic high-utility patterns. This paper successfully addresses the top-k mining issue and contributes to data science.