Abstarct: Small Area estimation (SAE) is the method of creating reliable and accurate estimates in the regions for which the use of direct estimation methods does not provide the required accuracy. The accuracy of estimation depends on the sample size, so the small sample size in small areas causes the accuracy of conventional direct estimates to decrease. SAE improves estimation in small regions by using auxiliary information and borrowing power from related and other sources. Generalized mixed effects models are often used in SAE due to their flexibility and interpretability. These models often have restrictive assumptions that may not be realized in practice. Presuppositions such as normality of random effects and errors, lack of measurement error of explanatory variables, independence and non-correlation of small areas, and linearity of relationships between the response variable and explanatory variables, can sometimes be violated in the estimation of small areas. Therefore, it is necessary to provide methods that increase the accuracy of estimations beyond these limitations. In this study, we have handled these limiting challenges by using i) semi-parametric spatial generalized linear mixed models, and ii) semi-parametric mixed-t models having measurement error. In the latter, the parameter estimation has been done by using both the EM algorithm and mexta-heuristic methods. Numerical studies are carried out to illustrate the superior performance of the proposed model in the prediction accuracy sense.