The correct option is
B He came to the school on time, but without his school books.
Option A: "However" is a conjunctive adverb which behaves like a co-ordinating conjunction. It is used to connect two independent clauses which contrast each other. It cannot be used along with the conjunction, "but" (which is also used to express contrast between two "words" or "phrases"). In option A, "but" and "however" are used together, which is grammatically incorrect. Hence, this option is incorrect.
Option B: "But" is a co-ordinating conjunction which is used two words/ phrases / clauses which contrast each other. Here, the phrase "without his school books' contrasts "came to the school". This is because one is expected to bring books to school. But the sentences express that he came to school without the books. Hence, they express contrast. Hence option B is correct.
Option C: "Not only... but also" is a correlative conjunction which is used to express two clauses which belong to the same parts of speech. This conjunction is used to connect two sentences which complement each other. Here, one sentence contrasts another. Hence, this option is incorrect.
Option D: "Despite" is a preposition which is used to show something which happened although something else might have prevented it. For example: "Despite my hard work, I failed in the examination". As it is not a conjunction, this option is incorrect.