Conformal prediction uses past experience to determine precise levels of confidence in new predictions. The proposed methodology allows for the construction of a distribution-free prediction bands for the response variable using any algorithm. The resulting prediction bands preserves marginal coverage guarantee, where predictive coverage holds on average over all possible test points, but is not sufficient for many practical applications. We aim to produce predictive conditional coverage rather than marginally with certain types of constrains and assumptions, while still being possible to achieve in a distribution-free setting.