Isotropic Quot scheme is a projective scheme that compactifies the moduli space of maps (of a given degree) from a smooth projective algebraic curve to an Isotropic Grassmannian. Isotropic quot schemes are often not smooth, but we construct a virtual fundamental class which makes it 'virtually' smooth. We use this to understand intersection theory of this space and find a Vafa-Intriligator type formula for the intersection of certain cohomology classes.