Correct Answer - Option 4 : Only I
The sentences suggest that the second part of the sentence is a direct result of the first.
The perfect participle phrase having + past participle form of the verb should be used here. It shows a completed action and joins the two sentences.
Correct Sentence:
Having developed an interest in native varieties, specifically the ones that grow without the use of fertilizers, he went on a quest for almost a year looking for such paddy varieties.
This is shown by I. So, a contextually coherent joined sentence is given by Only I.
None of the other phrase/s can make the sentence meaningful.
Therefore, the correct answer is option 4.