In support of what you're looking for...
On a clear September day in 2015, after 10 years of working to get funding, my colleague Kerry Key and I stepped aboard the R/V Langseth, a research ship docked at the Woods Hole Oceanographic Institution in Massachusetts. We were about to lead a 10-day expedition to map a deposit of fresh water, size unknown, hidden 100 meters (about 330 feet) under the rocky seafloor. (Source)
Freshwater aquifers can and do exist beneath the sea floor. And frankly, the more shallow the sea, the easier it would be to rationalize the aquifer.
A continent does not stop at its shoreline; it extends well offshore as a rocky underwater shelf. The shelf ends at a steep slope that transitions sharply to deep oceanic seafloor. The rock and sediments that make up the world's continental shelves are not dry. Some rocks crack, allowing seawater to penetrate. And most shelves are covered by layers of sedimentary rock, which are like hard sponges with small, interconnected, water-filled pores.
Sediments at or just below the seafloor are typically 40 to 50 percent porous. The weight of the ocean above pushes water down into the sediment as far as it can go. Geoscientists still debate the maximum depth, but it can be at least several kilometers, although the seepage decreases rapidly with depth as the increased pressure closes up cracks and pore spaces. The rock's permeability—the ease with which water can flow through it—depends on how extensively its various pores are interconnected.
Because the shelf is a continuation of the continent, models of groundwater flow in land along the northeastern U.S. coast suggest there could be substantial amounts of fresh water hidden within the rocks and sediments below the continental slope's seafloor. But there are competing hypotheses about how such water might get there—and remain there. (Ibid.)
@L.Dutch's answer, which I upvoted, makes a point, but it might not be the crisis he's suggesting.
It's easy to rationalize an undersea fresh water aquifer — but only when the ground beneath the aquifer isn't so messed up that it can't reasonably retain the water. Consider this image from the quoted article:
Credit: Julia Ditto; Source: “Origin and Extent of Fresh Paleowaters on the Atlantic Continental Shelf, USA,” by Denis Cohen et al., in Ground Water, Vol. 48; January-February, 2010 (reference). Image sourced from Rob L. Evans, "Found: Giant Freshwater Deposits Hiding under the Sea" (July 1, 2023).
In all those examples you'll see that the flow of rainwater from the land is contiguous. If you break that up with a fault line, you should expect the aquifer to end at the fault. Worse, the fault line represents a way for salt water to enter the undersea strata, meaning the aquifer will push less into the undersea region than it might otherwise have done.
I note that you describe the fault line (the subduction layer) under the mountains... not under the ocean. From a practical perspective, that means the water is running down the mountain and being absorbed into the undersea strata. Since the fault line is behind the aquifer, you don't have a problem. What you won't have is an aquifer on the other side of the mountains unless you allow sufficient rainfall on that side (in a continental context, the mountains could believably cause a continent-side rain shadow).
And a word about undersea artesian wells...
This is more believable than you might think, but not because of pressure. Again, from the linked article:
Records of fresh water being found offshore go as far back as the 1800s. Fishers off Florida have occasionally reported “boils” of water on the ocean's surface, which they assume leaked upward from below. In some cases, they sampled the water and it did not taste salty; fresh water is less dense than seawater, so it rises. (Ibid.)
In other words, you don't need pressure. You only need a leak and enough volume of fresh water that the press of salt water doesn't inundate the leak, causing that region of the aquifer to turn salty. Permeable, impermeable, kinda doesn't matter. By definition an aquifer forms because the water stops going down, not because it can't go up. In other words again, it means you can use the idea of impregnable rock as a story concept, but it's unnecessary for the science to work. All you really need is an easier path for the freshwater to enter the aquifer from land than for the saltwater to enter in the sea.