Single pole switch still controlling multiple lights

My dining room has a box on each wall with a single pole switch (for exterior light) next to a three way switch (for dining room interior light) that I attempted to replace with new switches. After changing all four switches out, all of the lights (two exterior lamps, dining room, kitchen, hallway, and bathroom) go out when I flip the first single pole exterior light switch off. This switch has 3 black wires connected to it which I’ve identified as the exterior switch, exterior hot, and the third is carrying power to the other light sources. I’ve tried wiring it multiple ways but it’s gotten me nowhere. Does anyone have an idea as to why this one single pole switch is controlling basically all of the general lighting in my house? Not sure what I did wrong. Any help would be greatly appreciated. Thanks

UPDATE

I did a pigtail of the supply and onward wires and attached the pigtail to the lower screw on the single pole switch, but the single pole switch is still controlling multiple lights. Very unsure what the issue could be. Would greatly appreciate any help. Thanks