Background checks

Hi everyone! I’m currently a 2nd year CS student at a state school and since March I’ve been interning part time at an early stage startup. Right now I’m an unpaid intern but this may change in the future. The company itself is not registered as a corporation. Would this affect my 2021 internship search / future job searches since the company is not incorporated and I don’t have any pay stubs or anything to show that I worked there? How does the background check process usually work for unpaid internships & how can I prove that I worked there?

Thank you!