Graphs are effective mathematical models for analyzing a variety of specific real-world issues. As a generalization of a graph, semigraph has also a pivotal role in graph theory. Because of its structure the idea of domination creates novel contributions in the field of network. In this article, we are trying to bring the concept of distance domination in connected semigraphs by defining l distance a-domination and l distance e-domination. The characterization of minimal l distance a-dominating set of connected semigraphs is also been discussed. Additionally l distance a-domination number, l distance e-domination number of some particular classes of semigraphs are determined.