The correct answer is option 4) i.e. yet. Explanation:
Let us explore the options:
'That' is a subordinating conjunction used to link a dependent clause to an independent clause, helping to show the relationship between the two clauses and emphasize the main idea of the freestanding/independent clause.
'When' is a subordinating conjunction. We use 'when' as a conjunction meaning to denote a time; 'at this time' or 'at a particular time.'
'Because' is subordinating conjunction used for showing the reason something happens or the reason why it is described in a particular way
'Yet' as a conjunction means ‘but’ or ‘nevertheless’. We use it to show contrast. It is a coordinating conjunction.
From the context of the sentence, the conjunction 'yet' should be used as there is a contrast between the phrases "He is sick" and "he wants to go to school".