In this research article, we study \(\ast\)-\(\eta\)-Ricci-Yamabe solitons on an \(\alpha\)-cosymplectic manifold by giving an example in the support and also prove that it is an \(\eta\)-Einstein manifold. In addition, we investigate an \(\alpha\)-cosymplectic manifold admitting \(\ast\)-\(\eta\)-Ricci-Yamabe solitons under some conditions. Lastly, we discuss the concircular, conformal, conharmonic, and \(W_2\)-curvatures on the said manifold admitting \(\ast\)-\(\eta\)-Ricci-Yamabe solitons.