Developer question and answering communities rely on experts to provide helpful answers. However, these communities face a shortage of experts. To cultivate more experts, the community needs to quantify and analyze the rules of the influence of extrinsic motivations on the ongoing contributions of those developers who can become experts in the future (potential experts). Currently, there is a lack of potential expert-centred research on community incentives. To address this gap, we propose a motivational impact model with self-determination theory-based hypotheses to explore the impact of five extrinsic motivations (badge, status, learning, reputation, and reciprocity) for potential experts. We develop a status-based timeline partitioning method to count information on the sustained contributions of potential experts from Stack Overflow data and propose a multifactor assessment model to examine the motivational impact model to determine the relationship between potential experts’ extrinsic motivations and sustained contributions. Our results show that (i) badge and reciprocity promote the continuous contributions of potential experts while reputation and status reduce their contributions; (ii) status significantly affects the impact of reciprocity on potential experts’ contributions; (iii) the difference in the influence of extrinsic motivations on potential experts and active developers lies in the influence of reputation, learning, and status and its moderating effect. Based on these findings, we recommend that community managers identify potential experts early and optimize reputation and status incentives to incubate more experts.