  We show the refinement of the prescription for the geometric transition in
the refined topological string theory and, as its application, discuss a
possibility to describe $qq$-characters from the string theory point of view.
Though the suggested way to operate the refined geometric transition has passed
through several checks, it is additionally found in this paper that the
presence of the preferred direction brings a nontrivial effect. We provide the
modified formula involving this point. We then apply our prescription of the
refined geometric transition to proposing the stringy description of doubly
quantized Seiberg--Witten curves called $qq$-characters in certain cases.
