Unlike comprehension-style questions, clarification questions look for some missing information in a given context. However, without guidance, neural models for question generation, similar to dialog generation models, lead to generic and bland questions that cannot elicit useful information. We argue that controlling the level of specificity of the generated questions can have useful applications and propose a neural clarification question generation model for the same. We first train a classifier that annotates a clarification question with its level of specificity (generic or specific) to the given context. Our results on the Amazon questions dataset demonstrate that training a clarification question generation model on specificity annotated data can generate questions with varied levels of specificity to the given context.