For/on summer session

For/on summer session
 

Are they all correct?

-Since taking summer courses is optional, the wait list information under BUSIS (name of an online system) will be removed after course registration period. Students must apply again for the courses offered under University Summer Session during the add/drop period.

For under, is it as correct as for, in, on, and during?

... under BUSIS ...
... in ...
... on ...

... after the course registration period.

... offered for the University Summer Session during ...
... offered under ...

Thank you, but do you think there's any difference in meaning between under, in and on? I would have thought under and in were not correct, because an online system (which is in fact a website) was used always with on, which my non-native friend told me. Can we also say in a website or under a website?

When you stated that BUSIS was an online system, I assumed it is an application and it is OK to specify that lists of data are in, on and under an application. 'Under' is the least likely preposition, by the way, in both sentences.

Do you mean Microsoft Word, Microsoft Powerpoint, etc.?

Yes. MS Word displays data on the screen. The data is stored in memory and is written to disk (stored on the hard drive).
When you use 'under' it is generally assumed to mean 'under control of' or 'in the format of' the application that displays/writes/stores/outputs the data.

Thank you.