In which countries must college professors be cleared to work with minors? I knew some college students in the U.S. who were &lt;18 years old.

In which countries must college professors be cleared (background-checked, certified, fingerprinted, etc., like U.S. K-12 teachers) to work with minors?
Any special requirements or background checks regarding working with minors are a matter of employer policy or local law, and there are no standard rules across different jurisdictions.  In particular, there's no way to give a definitive answer without knowing the exact circumstances.

As a general rule, though, these sorts of background checks are rarely applied to college faculty.  Even in locations with unusually strict laws, there are often exceptions for college professors, despite the fact that some students may be under 18.  For example, the University of Sydney policy explicitly says "Where University staff or affiliates have direct contact with University students under the age of 18, this is not regarded as child-related work under the Act."