i had an extra year gap between my class 10 and 12, will it have an influence on my SAT and admission process?
A gap year may affect your SAT and college admissions process, but only indirectly.
As far as the SAT goes, the most likely way that you'd be affected is if you're a little rusty on some of the concepts covered on the SAT because of your gap year. This is most likely to be true with the SAT Math section, since most of the content tends to be covered earlier on in high school; however, with review, that can be overcome. The only other issue that might arise is if you're older than the typical student who takes the SAT, because it might cause the College Board to flag you and double check that you're taking the test for the purposes of applying to college. We have more information about taking the SAT as an older student in this article.
The admissions process will also be a little different because you took a gap year, mainly because colleges are going to want to know what you did during your gap year. You might also have to put more effort into reconnecting with teachers for recommendations (although if the gap year is between two high school years, that's less likely to be an issue, since you'll presumably still be at the same school as your teachers). This article has some more advice on how to adjust for a gap year when applying to colleges.
I'd also recommend reading (if you haven't already) our blog article about gap years - some of the questions it raises about gap years (including potential issues and questions colleges might have) will be valuable for you to think about.