Summary: The object of the present paper is to study 3-dimensional \(\beta\)-Kenmotsu manifolds whose metric is Ricci soliton with respect to Schouten-van Kampen connection. We found the condition for the Ricci soliton structure to be invariant under Schouten-van Kampen connection. We have also showed that the Ricci soliton structure with respect to usual Levi-Civita connection transforms to a \(\eta\)-Ricci soliton structure under D-homothetic deformation. Finally we have shown that if a 3-dimensional \(\beta\)-Kenmotsu manifold admits a Ricci soliton structure with respect to Schouten-van Kampen connection and potential vector field as the Reeb vector field, then the manifold becomes \(K\)-contact Einstein.