The first name Jesse is ♀ female and ♂ male.
The unisex (mostly masculine) name Jesse is of Hebrew origin (Yishai/יִשַׁי, Old Testament: Jesse is the father of King David). Jesse is not related to the name Jessica.
Jesse means “gift of God” (from Hebrew “sháy/שַׁי” = present/gift), but as well “God exists” (from Hebrew “yésh/יֵשׁ” = there is/there exist).