This paper aims to examine a weighted class of function spaces, referred to as ${\mathcal{N}}_K(p,q)$-type spaces, defined on the unit ball of ${\mathbb{C}}^n$. The study explores the characterization of Carleson measures associated with these spaces and establishes embedding theorems connecting ${\mathcal{N}}_K(p,q)$-type spaces with weighted Hardy and Bergman spaces. In addition, applications involving Hadamard products and random power series within ${\mathcal{N}}_K(p,q)$-type spaces are discussed.