In this paper, we introduce the concept of ternary antiderivation on ternary Banach algebras and investigate the stability of ternary antiderivation in ternary Banach algebras, associated to the \((\alpha,\beta)\)-functional inequality: \begin{cases} &\| \mathcal{F}(x+y+z) - \mathcal{F}(x+z) - \mathcal{F}(y-x+z) - \mathcal{F}(x-z) \| \\ &\leq \| \alpha (\mathcal{F}(x+y-z) + \mathcal{F}(x-z) - \mathcal{F}(y)) \| + \| \beta (\mathcal{F}(x-z) \\ &+ \mathcal{F}(x) - \mathcal{F}(z)) \| \end{cases}where \(\alpha\) and \(\beta\) are fixed nonzero complex numbers with \(\vert\alpha \vert +\vert \beta \vert<2\) by using the fixed point method.