If one exists, I haven't seen it. I think it would be a fairly specialized config, because it is hard to distinguish mil dots spaced that close together on 4x. They are kinda tight even on 6x. If you are dead set on using a scope at 4x, and need mil dots, the closest thing I could think of is using a FFP 3-9x dialed down to 4x. It would almost need to be illuminated to be very useful for hunting. (Actually, the Vortex PST 2.5-10x32 would be excellent for that)
Another reason you may not see that configuration, is when hold-offs are needed due to getting out there a ways past 300 yards, magnification might ought to increase some. These days, with modern scopes being SO much better than 15 years ago, variables are very closely matched in durability and light transmission.
The SS fixed 6x is close to what you are looking for, but turrets might be a little bit big on a light hunting rig though. If you are set on fixed and 4x, IMO, the IOR hunting 4x is probably the best glass out there. I'd try to steer you that way, and if needed to reach way out there, uncap the elev turret and spin er up.
There are some mil-scale 1-4x24 variables that would be nice, like the mil/mil PST or Leupy VXR.