In this paper, we study the existence of periodic peaked solitons to a generalized \(\mu\)-Camassa-Holm-Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a \(\mu\)-version of a linear combination of the Camassa-Holm, modified Camassa-Holm, and Novikov equations. It is shown that the proposed equation admits a sigle peakons. It is natural extension of the previous results obtained in \cite{khe,moo,qu0} for the \(\mu\)-Camassa-Holm, modified \(\mu\)-Camassa-Holm, and \(\mu\)-Novikov equations, respectively.