Summary: A total \(k\)-labeling is a map that carries vertices and edges of a graph \(G\) into a set of positive integer labels \(\{1, 2,\dots, k\}\). An edge irregular total \(k\)-labeling of a graph \(G\) is a total \(k\)-labeling such that the weights calculated for all edges are distinct. The weight of an edge \(uv\) in \(G\) is defined as the sum of the label of \(u\), the label of \(v\) and the label of \(uv\). The total edge irregularity strength of \(G\), denoted by \(\mathrm{tes}(G)\), is the minimum value of the largest label \(k\) over all such edge irregular total \(k\)-labelings. In this paper, we investigate the total edge irregularity strength of generalized helm, \(H^m_n\) for \(n\geq 3\), \(m = 1, 2\), and \(m\equiv 0 \pmod 3\).