We introduce a parametrized version of the homotopic distance between maps, extending the notion introduced by Macías-Virgós and Mosquera-Lois to the fibrewise setting. Working in the category of fibrewise spaces over a fixed base space \(B\) , we define the parametrized homotopic distance \(D_B(f,g)\) between fibrewise maps and show that it admits an equivalent description in terms of the fibrewise sectional category of a canonical projection. This interpretation allows us to relate \(D_B(f,g)\) to the fibrewise Lusternik–Schnirelmann category and to the parametrized topological complexity. We establish the fundamental properties of the invariant, including fibre-homotopy invariance, behaviour under composition, triangle inequality, product inequalities, and cohomological lower bounds. For fibrewise fibrations, we obtain estimates for the parametrized homotopic distance in terms of the corresponding invariants on the fibres and the fibrewise LS category of the base, extending classical results of Varadarajan and Farber-Grant to the parametrized context. We also study maps into fibrewise H-spaces admitting a fibrewise division, deriving sharp estimates for the parametrized topological complexity in this setting and presenting explicit examples arising from sphere bundles. Finally, we introduce a pointed version of the parametrized homotopic distance, compare it with the unpointed invariant, and identify conditions under which both notions coincide.
