The doctor prescribed that the child must take/should take/take the medicine every 8 hours

Non-native here. The reason why this question confuses me is that this should be "took" based on what I have learnt in grammar classes. But that doesn't sound right. I am confused between take or must take. I feel it should be must since prescribed denotes authority. My friends are split between should take and take.

This is not the wording that is typically used in the UK. Normally you would say that "the doctor prescribed the medicine <as the object of 'prescribed' and then the dosage <in the form 'to be taken n times a day'>." So, for example:-

The doctor prescribed an antibiotic to be taken three times daily.

Given the particular phrasing one which you are working, the correct standard tense depends on the context to which the sentence applies.

Thus it might be that the the patient has just come out of the surgery with the prescription and is saying to the chemist (so before even starting the course of treatment)

The doctor prescribed that I must take the antibiotic three times a day.

Or it might be that something went wrong with the prescription and the patient go so ill that s/he is suing the doctor for damages. Both the medicine and the taking of the doses are fully in the past. Then you would expect:-

The doctor prescribed that I should take the antibiotic three times a day