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Let $\mathbb{K}$ be a complete ultrametric algebraically closed field and $\mathcal{A}\left( \mathbb{K}\right) $\ be the $\mathbb{K}$-algebra of entire function on $\mathbb{K}$. For any $p$-adic entire functions $f\in \mathcal{A}\left( \mathbb{K}\right) $ and $r>0$, we denote by $|f|\left(r \right) $ the number $\sup \left\{ |f\left( x\right) |:|x|=r\right\} $ where $\left\vert \cdot \right\vert (r)$ is a multiplicative norm on $\mathcal{A}\left( \mathbb{K}\right) .$ In this paper we study some growth properties of composite $p$-adic entire functions on the basis of their relative $\left( p,q\right) $-$\varphi $ order where $p$, $q$ are any two positive integers and $\varphi \left( r\right) $ $:$ $[0,+\infty)\rightarrow (0,+\infty )$ is a non-decreasing unbounded function of $r$.
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