The sentence which is written correctly is:
A. As an enthusiastic reader, Sanjay often visits the library to check out new books.
Usually, a comma appears after the dependent clause. Though the dependant clause contains verb and subject still it cannot stand alone. In the above sentence, the dependent clause is “ As an enthusiastic reader” after which the comma should appear. The comma here lays emphasis on the type of reader Sanjay is. Hence, this sentence is correctly punctuated.
