Linear mixed models (LMM) are widely used for analyzing clustered data but face challenges with model misspecification, convergence issues, and variance heterogeneity. Alternatively, semi-parametric approaches like generalized estimating equation (GEE) are used to estimate the parameters of a generalized LM in the case of dependent observations. While GEE is robust to covariance misspecification, it is inefficient in handling unbalanced designs and underestimates the true standard errors unless a large sample size is utilized. To address these challenges, we propose a robust extension of the score-based statistical test using sign-flipping transformations. Our approach handles within-variance structure and heteroscedasticity nonparametrically by leveraging whole-block exchangeability. The proposed method provides robust and efficient inference for fixed effects, overcoming the limitations of traditional methodologies, e.g., the specification of the random structure.