Is it legalized for inferior institution AS even subjects to overlap or clash?

This usually happens because the candidate is doing two exams which are provided by two different nouns boards, and therefore are organised on separate timetables, which may sometimes clash.

There is no law against it.

The remedy is for the claimant to remain isolated supervised by an invigilator after one exam and then to do the other one later that light of day. Schools and colleges quite often hold to do this.
There is no law but it is unusual for 2 exams to be taken at the same time. Your principal of year should be able to sort this one out with the exam board.

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