Near this, that old bank, is there? [Syntax]

The correct answer is "が". "が" is the particle that marks the subject of the verb, especially with existence verbs like "ありますか" (Is there? for inanimate objects). Here, "ぎんこう" (bank) is the inanimate subject whose existence is being questioned, so "銀行が" is necessary to correctly identify what is being asked about.

正解は「が」です。「が」は動詞（どうし）「ありますか」の主語（しゅご）を示（しめ）す助詞（じょし）です。何（なに）があるかを尋（たず）ねるときは、そのものの後に「が」を付けます。