How does Mikoto know about the Sisters before the Sister's Arc?
After Mikoto meets Nunotaba Shinobu, she starts investigating her and finds her connection with the 7th Medical Research Center, who were researching her DNA map to create an army of level 5 clones.

This is covered in the Railgun manga and Railgun S anime.

Initially she thought the Sisters project was abandoned because the clones would only be Level 3 (thus not realizing the plan for an army of Level 5 clones), but it's not until later that she realizes the Sisters were utilized for the Level 6 Shift project.