Summary: In this article we introduce the so called \(p\)-deformed algebra \(\mathcal{V}\). The notion of \(p\)-deformation is connected to the well-known \(q\)-deformation by the simple relation \(p = \frac{q^2+q^{-2}}{2}\). Thus the \(p\)-deformed algebra \(\mathcal{V}\) will have representations in terms of \(q\)-difference operators. There are isomorphisms of \(\mathcal{V}\) to the \(q\)-deformed Weyl algebra \(\mathcal{W}\) and to the well known algebra \(\mathcal{U} = \mathcal{U}_q\), the \(q\)-deformation of the universal enveloping algebra \(U_q(\mathfrak{sl}(2))\), extended by an involution. It turns out that the presentation of the \(p\)-deformed algebra \(\mathcal{V}\) is more symmetric than the ones of its \(q\) counterparts. Especially the limit \(p\to\pm1\) can be performed in a direct and quite consistent manner. For \(p^2 = 1\) the \(p\)-deformed algebra contains copies of the classical Weyl algebra, the Lie superalgebra \(\mathfrak{osp}(1|2)\) and the Lie algebra \(\mathfrak{sl}(2)\). Finally we will see that the \(p\)-deformed algebra \(\mathcal{V}\) contains a ``squared copy'' of itself.