What kind of education do congressmen in the legislative branch have to have?
There are no educational requirements at all in the Constitution, for any branch of government, only age minimums and citizenship requirements, for a congressman, the minimum age of 25 and a requirement of citizenship for no less than seven years.
When the Constitution was created, most people did not have formal educations at all, and such a requirement would have prevented many fine people from serving in Congress. We live in a different world today, where most people have a high school education and many people have at least a bachelor's degree. Most of the people in Congress do have a college education, and many of them are attorneys, so some people assume that college is a minimum requirement, while others may assume that law school is required. In fact, someone who had no high school education would not be barred from serving in Congress on that basis, and in the early days of our country, there probably were many legislators who were entirely self-educated.
To change this and require some minimum education would necessitate a constitutional amendment, and it is difficult to say, first, if it could be passed, and second, whether it would improve the quality of members of Congress. In spite of how highly I value education, I am inclined to think it would make very little difference, and it is possible it would make things even worse, since we would be even less likely to have any representatives but the wealthy.