My fleet seems to be going station to station around my system, wasting gas. I just want them to sit.
I hit stop and they continue...
Their current mission is "none"..
Everything I know of is set to control manually.
I don't see any setting making them do this. What could it be?
They are patrolling because something told them to patrol. Either you or some automation that can be turned off. Automated fleet? Fleet formation automated? War and attack automated? Some of that could cause it, I don't have this issue.
I have a hard time with my fleet, as well. I was attacking a colony with a couple dozen ships, and my ships kept flying off piecemeal to attack mining bases in the system. I tried setting their stance to defense, turning off automation, telling them to stop, everything I could to prevent ships from flying away from the fleet to attack bases I didn't want them to attack, but just had to sit there clicking like crazy herding them back to the main fleet.
There is no way to avoid this without excessive micro management. Any ship with no mission will usually "attack system targets". They will gang up according to the setting in empire polity of attack overmatch, which may decide whether 1 or 5 jump at each mine (see options - empire policy). You can try to change their attack stance (a button around the selection panel) to something else than "attack system targets" but from one that has tried to control fleets in enemy systems for years:
Don't try to have a fleet hang around in a system with enemy structures. If they are mines, let them kill them, if they are a large spaceport with friends and you want to hang around in the outskirts, kill the spaceport or leave the system before it kill your ships. You can keep the fleet busy, though, by telling it to jump around in the system, or to tell it to chain-kill all the mining bases and then refuel. But you can not in a sane way make them sit around with something to kill inside the system. And if you make them chain kill stuff including defenders, and see them happily engaging the enemy ships? One of them is going to kill its target or find that it is "free" due to attack overmatch being met and think: "Ey, they can handle this! I can go kill that large spaceport instead".
I usually want my ships to sit on top of whatever they defend. So that they are right there when nasties appear. Whether it is defending a gas mine from pirates in early game, or defending a colony from raid or invasion, having to start off from the other side of the system is not a good start on a protection duty. This is a partly losing battle, the fleet loves to jump at some enemy exploration ship in the system, or something else they feel they have to attack. So one has to herd them back. Or one has to find some wonderful automation setting that I have yet to find.