While machine learning is making significant advances in recent years, the problem of its theoretical understanding still remains an open challenge. One key aspect is the ability to predict the generalization of learning algorithms' predictions, which is crucial for assessing their reliability in various domains such as medicine, biology, finance, and signal processing. Previous studies in supervised learning have considered, in the vast majority of cases, Gaussian distributed covariates. However, in practical applications of machine learning, the data distribution may diverge from Gaussianity in many ways, such as fluctuations, heavy-tails or structured patterns. This work aim to investigate, employing the heuristic replica method from statistical physics, the supervised learning of generalized linear models when the covariates are distributed according to a superstatistical model, meaning that each covariate is drawn from a Gaussian distribution with random covariance following a generic probability distribution ρ.