  In this note I define an overconvergent version of prisms and prismatic
cohomology as introduced by Bhatt and Scholze and show that overconvergent
prismatic cohomology specialises to $p$-adic cohomologies, like
Monsky-Washnitzer resp. rigid cohomology for smooth varieties over a perfect
field, the de Rham cohomology of smooth weak formal schemes over a perfectoid
ring and the \'{e}tale cohomology of its generic fibre. Besides, I give an
overconvergent version of the complex $A\Omega$ of Bhatt-Morrow-Scholze and
relate it to overconvergent prismatic cohomology.
