In the System or On the System
Happy holidays, Pavel Alexandrovich and Sima!
'In the system' and 'on the system' are both correct, but have different usage. Use 'in the system' when referring to something that is contained or included within the system.
For example:
The data is stored in the system. Or, there is a bug in the system. (The 'data' and the 'bug' were already in the system.)
'On the system' is used when referring to something that is located or accessible on the system.
For example:
You can find the file on the system. The document is saved on the system. (The 'file' and the 'document' were placed on the system and were not originally part of it.)