I started my period during sex on sept 21,it lasted 5 days on october 2 i had sex. my due date 6/20/2015,did i get pregnant on my period?

Not likely at all: If your due date is indeed estimated to be 6-20-2015 (+ or - 10 days) and was confirmed by accurate and reliable first trimester sonograms, you probably had ovulated about 9-27 and therefore would have gotten pregnant around that time (+ or - a few days) . You may have had some irregular "vaginal bleeding" but did do not get pregnant on your period.