I’m pretty sure that your only option is
It’s an Aquantia chipset, I don’t know of any Intel chips that have a Gen4x1 lane configuration at 10GbE. This card does claim to have Linux support, though with little detail.
Note the physical PCIe fingers are actually x2, so I think you’d need to have an open-ended x1 slot or be wiling to take some snips to it or such to fit the card.