Motivation: Estimation of the hidden population structure is an important step in many genetic studies. Often the aim is also to identify which sequence locations are the most discriminative between groups of samples for a given data partition. Automated discovery of interesting patterns that are present in the data can help to generate new biological hypotheses. Results: We introduce Kpax3, a Bayesian method for bi-clustering multiple sequence alignments. Influence of individual sites will be determined in a supervised manner by using informative prior distributions for the model parameters. Our inference method uses an implementation of both split-merge and Gibbs sampler type MCMC algorithms to traverse the joint posterior of partitions of samples and variables. We use a large Rotavirus sequence dataset to demonstrate the ability of Kpax3 to generate biologically important hypotheses about differential selective pressures across a virus protein. Availability and Implementation: Kpax3 is implemented as a Julia package and released under the MIT license. Source code and documentation are available at: https://github.com/albertopessia/Kpax3.jl