The issue of model-based clustering of longitudinal data has attracted increasing attention in past two decades. Finite mixtures of Student's-t linear mixed-effects (FM-tLME) models have been considered for implementing this task especially when data contain extreme observations. This paper presents an extended finite mixtures of Student's-t linear mixed-effects (EFM-tLME) model, where the categorical component labels are assumed to be influenced by the observed covariates. As compared with the naive methods assuming the mixing proportions to be fixed but unknown, the proposed EFM-tLME model exploits a logistic function to link the relationship between the prior classification probabilities and the covariates of interest. To carry out maximum likelihood estimation, an alternating expectation conditional maximization (AECM) algorithm is developed under several model reduction schemes. The technique for extracting the information-based standard errors of parameter estimates is also investigated. The proposed method is illustrated using simulation experiments and real data from an AIDS clinical study.