<p>The present article involves the study of linear positive operators associated with adjoint Apostol-type Frobenius-Euler polynomials. Initially, we introduce the univariate operators and calculate their moments. We establish Korovkin-type theorems using two different sets of test functions. Then we derive a Voronovskaya-type formula for the class of functions having exponential growth. Moreover, we introduce the corresponding bivariate operators and study their pointwise convergence. Additionally, we present quantitative estimates in terms of the first- and second-order moduli of smoothness, as well as the weighted modulus. Finally, we examine the rates of convergence for both operators via graphical examples.</p>