In this study, we employ density functional theory along with the artificial bee colony algorithm for cluster global optimization to explore the low-lying structures of TeBnq (n = 3-16, q = 0, -1). The primary focus is on reporting the structural properties of these clusters. The results reveal a consistent doping pattern of the tellurium atom onto the in-plane edges of planar or quasi-planar boron clusters in the most energetically stable isomers. Additionally, we simulate the photoelectron spectra of the cluster anions. Through relative stability analysis, we identify three clusters with magic numbers -TeB7-, TeB10, and TeB12. The aromaticity of these clusters is elucidated using adaptive natural density partitioning (AdNDP) and magnetic properties analysis. Notably, TeB7- exhibits a perfect σ-π doubly aromatic structure, while TeB12 demonstrates strong island aromaticity. These findings significantly contribute to our understanding of the structural and electronic properties of these clusters.