stalk of a leaflet.
Merriam-Webster Online Dictionary
petiolule (noun) a stalk of a leaflet of a compound leaf
petiolule (Wikipedia)
Leaf of dog rose (Rosa canina), showing the petiole, two leafy stipules, the rachis, and five leaflets
In botany, the petiole (/ˈpiːtioʊl/) is the stalk that attaches the leaf blade to the stem. Outgrowths appearing on each side of the petiole in some species are called stipules. Leaves lacking a petiole are called sessile or epetiolate.