Summary: We establish the notion of \(\tau\)-generalized contraction for a pair of mappings \(S_1\) and \(S_2\) over a set \(Z\), where \(\tau : Z^2\to [1, +\infty)\) is a function. We appoint our new notion to formulate and prove many common fixed point results in the setting of generalized \(b\)-metric spaces. Examples are provided to analyze our results. Also, we set up applications to show the importance of our results. Our results are modification for many exciting results in the literature.