Let \(F\) be a number field or a \(p\)-adic field. The author introduces in Chapter 2 of this work two reductive rank one \(F\)-groups, \(\mathbf{H_1}\), \(\mathbf{H_2}\), which are twisted endoscopic groups of \(\mathrm{GSp}(2)\) with respect to a fixed quadratic character \(\varepsilon\) of the idèle class group of \(F\) if \(F\) is global, \(F^\times\) if \(F\) is local. When \(F\) is global, Langlands functoriality predicts that there exists a canonical lifting of the automorphic representations of \(\mathbf{H_1}\), \(\mathbf{H_2}\) to those of \(\mathrm{GSp}(2)\). In Chapter 4, the author establishes this lifting in terms of the Satake parameters which parameterize the automorphic representations. By means of this lifting he provides a classification of the discrete spectrum automorphic representations of \(\mathrm{GSp}(2)\) which are invariant under tensor product with \(\varepsilon\).