According to the Swisscom network coverage map, an impeccable 2G, 3G and 4G connection should actually be available in Stabio.
Of course, it is also possible that if you move closer to the border, there will be some kind of overlap.
What I propose to you is to try to switch the network operator from automatic to Swisscom manually. Now depends on what device you have. If you tell us what it is, I can tell you how to set it up.
Otherwise, if that doesn't work, I would also try to activate limits such as roaming - if your subscription allows it. And if that is not an option, I would call the hotline on 0800 800 800.