  Plateaued functions as an extension of bent functions play a significant role
in cryptography, coding theory, sequences and combinatorics. In 2019,
Hod\v{z}i\'{c} et al. designed Boolean plateaued functions in spectral domain
and provided some efficient construction methods in spectral domain. However,
in their constructions, the Walsh support of Boolean $s$-plateaued functions in
$n$ variables contains at least $n-s$ columns corresponding to affine functions
on $\mathbb{F}_{2}^{n-s}$. In this paper, we study generalized $s$-plateaued
functions from $V_{n}$ to $\mathbb{Z}_{p^k}$ where $p$ is an odd prime and
$k\geq 1$ or $p=2, k\geq 2$ and $n+s$ is even. Firstly, inspired by the work of
Hod\v{z}i\'{c} et al., we give a complete characterization of generalized
plateaued functions with affine Walsh support and provide some construction
methods of generalized plateaued functions with (non)-affine Walsh support in
spectral domain. In our constructions, the Walsh support can contain strictly
less than $n-s$ columns corresponding to affine functions and our construction
methods are also applicable to Boolean plateaued functions. Secondly, we
provide a generalized indirect sum construction method of generalized plateaued
functions, which can also be used to construct (non)-weakly regular generalized
bent functions. In particular, we show that the canonical way to construct
Generalized Maiorana-McFarland bent functions is a special case of the
generalized indirect sum construction method and we illustrate that the
generalized indirect sum construction method can be used to construct bent
functions not in the complete Generalized Maiorana-McFarland class.
Furthermore, based on this construction method, we give constructions of
plateaued functions in the subclass WRP of the class of weakly regular
plateaued functions and vectorial plateaued functions.
