Is it legal for a public university to deny me admittance due to having a mental illness if i meet or exceed the standard of all other applicants?

There is no simple answer to this; much will depend on the characterof th mental illness. If there is reason to believe, for example, that you pose a hazard to other students or staff members, that could justify their actions. Since this is a very-fact-specific question, you should consult with an attorney in experience in discrimination cases in education--particularly against the disabled--who can review the specifics of your situation in detail.