How do you plan on carrying a fixed blade while on duty? There are several types that are applicable to different styles. I carry a Cold Steel Peace Keeper II on my SWAT plate carrier. It comes with a plastic sheath, which is paracorded through the Molle in an inverted position. That's not exactly practical for every day patrol carriers though. Are you looking for a small fixed blade for your belt? Like a claw style or something? Or maybe a neck knife to wear under your uniform as a last resort weapon...? Or a boot knife? Or maybe all of the above..? As you can see there are a lot of considerations.
For patrol style work I'd prefer something a little more concealable for a fixed blade because chances are it's a last resort weapon. I personally would not wear a fixed blade on my gun belt for several reasons: the only real place to put it is opposite your gun side, most likely toward the front. Someone looking for a fight will focus on your gun belt because they know everything that can hurt them is coming from there. A handle sticking out of a plastic sheath would be the first thing I would go for if I was a bad guy...especially knowing most officers will first protect their gun side. Chances are the retention won't be very secure and during a scuffle or wrestling match it's a liability...sure, it may be easily accessible for you..but that also means it is for the bad guy.
A pocket knife will handle all the EDC responsibilities during normal duty, so for a fixed blade I'd just worry more about what is comfortable and convenient and what you'll actually keep putting on every day. If you get something large, uncomfortable or cumbersome it doesn't matter what the steel or edge style is because you'll quit wearing it. I never wore a fixed blade on patrol, but if you could find a comfortable boot knife, that would probably be a good bet. Sorry I don't have a good suggestion on the actual knife...but once you narrow down the type there are plenty of people here to help you pick one out.
And this is all different for firefighters and military I'm sure...