For an endomorphism ${alpha}$ of a ring R, the endomorphism ${alpha}$ is called semicommutative if ab=0 implies $aR{alpha}(b)$=0 for a ${in}$ R. A ring R is called ${alpha}$-semicommutative if there exists a semicommutative endomorphism ${alpha}$ of R. In this paper, various results of semicommutative rings are extended to ${alpha}$-semicommutative rings. In addition, we introduce the notion of an ${alpha}$-skew power series Armendariz ring which is an extension of Armendariz property in a ring R by considering the polynomials in the skew power series ring $R[[x;;{alpha}]]$. We show that a number of interesting properties of a ring R transfer to its the skew power series ring $R[[x;;{alpha}]]$ and vice-versa such as the Baer property and the p.p.-property, when R is ${alpha}$-skew power series Armendariz. Several known results relating to ${alpha}$-rigid rings can be obtained as corollaries of our results.