I believe that "intra" would be the closest thing to an antonym for "inter".
For example, an intERschool sports day would involve students from different schools competing against each other, whereas an intRAschool sports day would involve students from the same school competing against each other.
Inter - between (i.e. between two different things such as interschool being between different schools)
Intra -within (such as intra school being within one school)
(not to be confused with inFra, which means 'under')
'extra' is also used, but depending on the context it may not work i.e. extra-net? (intranet is the actual word for a network within say a company that is not accessible to the outside world). extra-sex? (I'm not sure, but I'd go with intra-sex rather than extra-sex. Extra just sounds weird there.)
Hope that helps!