In the present manuscript, we study the oscillation theory for a first-order nonlinear neutral dynamic equations on timescales with variable exponents of the form. (Formula presented.) where ξ is a quotient of odd positive integers; (Formula presented.) be a fixed number; (Formula presented.) is a timescale interval; η,τm > 0; (Formula presented.) for m = 1,2,…,n such that (Formula presented.), and the variable exponents αm(t) satisfy (Formula presented.). The principal goal of this paper is to establish some new succinct sufficient conditions for oscillation. Furthermore, we introduce a forcing term (Formula presented.) and then study the oscillation. Afterward, some interesting special cases are also studied to obtain similar sufficient conditions of oscillation under certain conditions. Moreover, the oscillatory behaviour of the solutions of a first-order neutral dynamic equation on timescale with a nonlocal condition and a forced nonlinear neutral dynamic equation on time scale are studied. But the proofs are based on the prior estimates obtained in this paper. Some enthralling examples are constructed to show the effectiveness of our analytic results. These counterparts are quite different in the literature even when T = R. Finally, the Kamenev-type and Philos-type oscillation criterions are established.