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This work examines a class of path-dependent stochastic systems which are hybrid with wideband noise, Poisson jumps and a singularly perturbed Markov chain. The addition of multi-scale Markov chain allows for modeling of discrete events with both fast and slow fluctuation. While this more realistic approach presents analytical challenges due to the non-Markovian formulation resulting from the wideband noise and the singularly perturbed Markov chain. By virtue of the weak convergence method and Itô functional formula, we prove that as ɛ → 0 , we obtain a Markovian switching jump diffusion. Finally, we offer several examples to illustrate our findings. • This is the first time to consider a class of stochastic systems with hybrid switching, wideband noise, Poisson jumps as well as time-delay perturbations. • Two-time-scale Markovian chain can describe the systems with both strong and weak interactions, which becomes really helpful when we dealt with a large-scale system. • Our problem is path-dependent and its phase space is infinite-dimensional, functional Itô formula expected to be applied to deal with such complex situation. • By virtue of the weak convergence method and Itô functional formula, we get the limit system for the singularly perturbed functional systems. • Integro-differential systems, Ginzburg–Landau equations and Replicator dynamics are presented to illustrate our findings. [ABSTRACT FROM AUTHOR]