We analyze here displacement controlled peeling of a flexible adherent off a thin layer of elastic adhesive, the elastic modulus of which does not remain uniform but varies periodically along the direction of peeling. Calculation shows that with progressive peeling, the crack front does not propagate continuously at the interface but intermittently with crack arrests and subsequent initiations. The crack gets arrested close to the location of the minimum shear modulus of the layer and initiates again only at a sufficiently large peel off load. This effect is very similar to the peeling experiment off surface patterned and microchannel embedded adhesives which results in significant enhancement of fracture toughness of the interface over smooth adhesive layers. The fracture toughness of the interface increases with the increase in thickness of the layer and the amplitude of variation in modulus. Fracture toughness is calculated to be high also for the larger value of critical stress at the opening of the crack. With the wavelength of modulus variation, it varies nonmonotonically, maximizing at an intermediate value. These results define the criterion for designing adhesive layers with spatially modulated physical properties useful for variety of applications.