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Advances in high-throughput biotechnologies have culminated in a wide range of omics (such as genomics, epigenomics, transcriptomics, metabolomics, and metagenomics) studies, and increasing evidence in these studies indicates that the biological architecture of complex traits involves a large number of omics variants each with minor effects but collectively accounting for the full phenotypic variability. Thus, a major challenge in many "ome-wide" association analyses is to achieve adequate statistical power to identify multiple variants of small effect sizes, which is notoriously difficult for studies with relatively small-sample sizes. A small-sample adjustment incorporated in the kernel machine regression framework was proposed to solve this for association studies under various settings. However, such an adjustment in the generalized linear mixed model (GLMM) framework, which accounts for both sample relatedness and non-Gaussian outcomes, has not yet been attempted. In this study, we fill this gap by extending small-sample adjustment in kernel machine association test to GLMM. We propose a new Variant-Set Association Test (VSAT), a powerful and efficient analysis tool in GLMM, to examine the association between a set of omics variants and correlated phenotypes. The usefulness of VSAT is demonstrated using both numerical simulation studies and applications to data collected from multiple association studies. The software for implementing the proposed method in R is available at https://www.github.com/jchen1981/SSKAT., (© 2021 Wiley Periodicals LLC.)