In this paper, I establish a new type of modal disjunction system in Korean. Thus far, (i)na has been considered as a typical modal disjunctive particle. Introducing inka as a new type of modal disjunctive particle, I propose that the class of Koran modal disjunctive particles is not homogeneous, and there should be fi ne-grained distinction system. Considering that (lack of) epistemic knowledge of the speaker is one of the possible dimensions of variation within the class of modal disjunction, my proposal on the use of inka is identified as an irrealis marker (Mauri 2008) which specifies alternative disjuncts with irrealis value. I further show that the epistemic constraint of inka on the irrealis value is characterized as a condition of minimal variation and uncertainty of anti-specific disjunction in the sense of Giannakidou and Quer (2013).