Abstract We perform a Bayesian study of a generalization of the basic α -attractor T model given by the potential V ( ϕ ) = V 0 1-sech p ( ϕ /√(6 α ) M pl ) where ϕ is the inflaton field and the parameter α corresponds to the inverse curvature of the scalar manifold in the conformal or superconformal realizations of the attractor models. Such generalization is characterized by the power p which includes the basic or base model for p = 2. Once the priors for the parameters of the α -attractor potential are set by numerical exploration, we perform the corresponding statistical analysis for the cases p = 1, 2, 3, 4, and derive posteriors. Considering the original α -attractor potential as the base model, we calculate the evidence for our generalization, and conclude that the p = 4 model is preferred by the CMB data. We also present constraints for the parameter α . Interestingly, all the cases studied prefer a specific value for the tensor-to-scalar ratio given by r ≃ 0.0025.