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 (/ˈptil/) 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.

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