If I do well in the first quarter of the senior year, does this increase my chance of getting in or do they only look at first semester of senior grade.
If I am reading your post correctly, you are asking whether quarter grades from second semester senior year, which are provided likely sometime in March of senior year, can help in getting admitted… For most colleges that have real application deadlines, the last possible grades that will be used for admission are first semester grades and many of those, including a lot of public universites, actually make admisison decisions only with grades through junior year. Grades from second semester senior year are used only in June or July, after you have been admitted and have submitted your final high school transcript, to determine if the admisison given should be withdrawn.
Some colleges, none of any real rank or being difficult to get into, accept applications for fall admission into the summer after your senior year and as late as July or early August, and for those your second semester senior year grades can be part of the consideration for admission it you apply that late.
The college you matriculate to will want your final high school transcript showing your second semester grades.
Its admission will be conditional on it showing the same courses you previously reported as in progress, with high enough grades in them. The definition of “high enough” varies. Some colleges give explicit grade and GPA thresholds, while others give a more vague expectation of similar academic achievement as before.
Do at least as well as you did before, and do not get any D or F grades, to minimize the risk of admission rescission based on your last semester of high school.
Colleges have the right to rescind your acceptance if you bomb out second semester senior year. Generally that means no Ds or F’s. (One poster on CC says "no Ds, Fs or felonies). I’d suggest trying to keep grades in the B range if possible.
Should you find yourself on a WL for a school you want to attend, and should you choose to pursue admission, your grades in the second semester of senior year could definitely help push you to the head of the list if you are doing well.
Should you decide to transfer, those grades will be completely visible to your transfer targets.
Personally, my advice is to keep working. It’s not just about the grades, but developing a good foundation for college, both academically and in your habits.