The discussion of n-generalized is a fundamental challenge in mathematical discussions. Considering that a lot of attention has been paid to this discussion in recent years and studies, it is clear that there are still many and various challenges in this field. In this paper we investigate and presented n-generalized skew projection for n=2,3 in Banach algebras. All the equations are given completely from the beginning and the basis, and the full explanation of each of the formulas along with their proof is presented in the paper. Also, all relevant issues have been fully discussed and discussed in the paper. Necessary and sufficient conditions for a linear combination of two n-generalized skew projection for n=2,3 to be a n-generalized skew projection for n= 2,3 are developed. Our results generalize results obtained for bounded linear operators on Hibert spaces. Also, all relevant issues have been fully discussed and discussed in the article.