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Recommendation systems (RS) play a crucial role in assisting decision-making but often suffer from either a lack of credibility or unfairness problems. A few recommendation models have endeavored to address the problem from only one aspect, and approaches to solving both problems remain to be explored. This paper aims to construct a generalized fairness-based recommendation framework that can also provide the credibility of recommendation models. Generally, we propose a reliable and fair recommendation framework called Conformalized User Group Fairness (CUGF) based on the inspiration of conformal prediction. Specifically, we construct dynamic prediction sets that are guaranteed to cover the true item with a user pre-specified probability to ensure credibility while designing novel fairness metrics based on empirical risks to guarantee the fairness of users across different groups. Furthermore, we design a novel CUGF Algorithm to optimize the parameter γ that dominates the prediction sets and also the fairness. Besides, we conduct extensive experiments by applying CUGF on top of various recommendation models and representative datasets to validate its effectiveness with respect to recommendation performance (in terms of average set size) and fairness (in terms of the two defined fairness metrics), the results of which demonstrate the validity of the proposed framework.