  The object of this paper is to introduce and study properties of unified
Apostol-Bernoulli and Apostol-Euler polynomials noted by
$\left\{\mathfrak{V_{n}}(x;\lambda;\mu)\right\}_{n \geq 0}$. We study some
arithmetic properties of $\left\{\mathfrak{V_{n}}(x;\lambda;\mu)\right\}_{n
\geq 0}$ as their connection to Apostol-Euler polynomials and Apostol-Bernoulli
polynomials. Also, we give derivation and integration representations of
$\left\{\mathfrak{V_{n}}(x;\lambda;\mu)\right\}_{n \geq 0}$. Finally, we use
the umbral calculus approach to deduce symmetric identities.
