In high-throughput profiling studies, extensive efforts have been devoted to searching for the biomarkers associated with the development and progression of complex diseases. The heterogeneity of covariate effects associated with the outcomes across subjects has been noted in the literature. In this paper, we consider a scenario where the effects of covariates change smoothly across subjects, which are ordered by a known auxiliary variable. To this end, we develop a penalization-based approach, which applies a penalization technique to simultaneously select important covariates and estimate their unique effects on the outcome variables of each subject. We demonstrate that, under the appropriate conditions, our method shows selection and estimation consistency. Additional simulations demonstrate its superiority compared to several competing methods. Furthermore, applying the proposed approach to two The Cancer Genome Atlas datasets leads to better prediction performance and higher selection stability.