Block-Göttsche polynomials establish connections between complex and real enumerative invariants via tropical geometry. Floor diagrams are oriented weighted graphs featuring particular combinatorial structures, which can be used to compute the Block-Göttsche polynomials. In this talk, I will introduce a q-refined correspondence theorem between higher genus relative Gromov-Witten invariants with a Lambda class insertion and the refined counts of higher genus floor diagrams relative to a conic. I will also present a Caporaso-Harris type recursive formula for the refined counts of higher genus floor diagrams, along with an application of the correspondence theorem on the generalization of higher genus Block-Göttsche polynomials. This is a joint work with Jianxun Hu.