  We consider a deformation of a family of hyperelliptic refined spectral
curves and investigate how deformation effects appear in the hyperelliptic
refined topological recursion as well as the $\mathscr{Q}$-top recursion. We
then show a coincidence between a deformation condition and a quantisation
condition in terms of the $\mathscr{Q}$-top recursion on a degenerate elliptic
curve. We also discuss a relation to the corresponding Nekrasov-Shatashivili
effective twisted superpotential.
