Quantum technologies would benefit from the development of high-performance quantum defects acting as single-photon emitters or spin-photon interfaces. Finding such a quantum defect in silicon is especially appealing in view of its favorable spin bath and high processability. While some color centers in silicon have been emerging in quantum applications, there remains a need to search for and develop new high-performance quantum emitters. By searching a high-throughput computational database of more than 22,000 charged complex defects in silicon, we identify a series of defects formed by a group III element combined with carbon ((A-C)Si with A = B, Al, Ga, In, Tl) and substituting on a silicon site. These defects are analogous structurally, electronically, and chemically to the well-known T center in silicon ((C-C-H)Si), and their optical properties are mainly driven by an unpaired electron on the carbon p orbital. They all emit in the telecom, and some of these color centers show improved properties compared to the T center in terms of computed radiative lifetime, emission efficiency, or smaller optical linewidth. The kinetic barrier computations and previous experimental evidence show that these T center-like defects can be formed through the capture of a diffusing carbon by a substitutional group III atom. We also show that the synthesis of hydrogenated T center-like defects followed by a dehydrogenation annealing step could facilitate the formation of these defects. Our work motivates further studies on the synthesis and control of this new family of quantum defects and demonstrates the use of high-throughput computational screening to discover new color center candidates.