  For prime $p$, $GR(p^a,m)$ represents the Galois ring of order $p^{am}$ and
characterise $p$, where $a$ is any positive integer. In this article, we study
the Type (1) $\lambda$-constacyclic codes of length $4p^s$ over the ring
$GR(p^a,m)$, where $\lambda=\xi_0+p\xi_1+p^2z$, $\xi_0,\xi_1\in T(p,m)$ are
nonzero elements and $z\in GR(p^a,m)$. In first case, when $\lambda$ is a
square, we show that any ideal of
$\mathcal{R}_p(a,m,\lambda)=\frac{GR(p^a,m)[x]}{\langle
x^{4p^s}-\lambda\rangle}$ is the direct sum of the ideals of
$\frac{GR(p^a,m)[x]}{\langle x^{2p^s}-\delta\rangle}$ and
$\frac{GR(p^a,m)[x]}{\langle x^{2p^s}+\delta\rangle}$. In second, when
$\lambda$ is not a square, we show that $\mathcal{R}_p(a,m,\lambda)$ is a chain
ring whose ideals are $\langle (x^4-\alpha)^i\rangle\subseteq
\mathcal{R}_p(a,m,\lambda)$, for $0\leq i\leq ap^s$ where $\alpha^{p^s}=\xi_0$.
Also, we prove the dual of the above code is $\langle
(x^4-\alpha^{-1})^{ap^s-i}\rangle\subseteq \mathcal{R}_p(a,m,\lambda^{-1})$ and
present the necessary and sufficient condition for these codes to be
self-orthogonal and self-dual, respectively. Moreover, the Rosenbloom-Tsfasman
(RT) distance, Hamming distance and weight distribution of Type (1)
$\lambda$-constacyclic codes of length $4p^s$ are obtained when $\lambda$ is
not a square.
