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Most globular clusters (GCs) show evidence for multiple stellar populations, suggesting the occurrence of several distinct star-formation episodes. The large fraction of second population (2P) stars observed requires a very large 2P gaseous mass to have accumulated in the cluster core to form these stars. Hence the first population of stars (1P) in the cluster core has had to become embedded in 2P gas, just prior to the formation of later populations. Here we explore the evolution of binaries in ambient 2P gaseous media of multiple-population GCs. We mostly focus on black hole binaries and follow their evolution as they evolve from wide binaries towards short periods through interaction with ambient gas, followed by gravitational-wave (GW) dominated inspiral and merger. We show this novel GW-merger channel could provide a major contribution to the production of GW-sources. Finally, our results suggest that the conditions and binary properties in the early stage of GCs could be critically affected by gas-interactions and may require a major revision in the current modeling of the evolution of GCs.