  We bring cocycle enhancement theory to the case of psyquandles. Analogously
to our previous work on virtual biquandle cocycle enhancements, we define
enhancements of the psyquandle counting invariant via pairs of a biquandle
2-cocycle and a new function satisfying some conditions. As an application we
define new single-variable and two-variable polynomial invariants of oriented
pseudoknots and singular knots and links. We provide examples to show that the
new invariants are proper enhancements of the counting invariant are are not
determined by the Jablan polynomial.
