Not quite enough info but I'll try to help. You said cleaning but not whether it's range cleaning or end of day. I'll start at the end. For end of day cleaning take the barrel off remove the nipple and put breech end in a bucket of warm (not hot) water with a little bit of dish or laundry soap in it. Dip your patch in the bucket to wet it and use a pumping motion as you progress down the barrel. DO NOT use a dry patch. That should take care of the stuck patch issue.
At the range start with a very wet patch and only go 1/2-3/4 way down the barrel and then change your patch to get rid of some of the gunk. Then a new saturated patch to go all the way down. You are probably getting a crud ring just above the powder level. If it still gets jammed, pour a little liquid something, I've used cleaning solution or gun oil, down the barrel to soften the fouling. A lot of times that's all that's needed. If still stuck I use a small piece of leather on the muzzle to protect it and then use my multi-tool pliers. Fit the pliers resting on the leather & perpendicular to the rod and lever the rod up a little at a time. You only have to lever it up enough to get the patch turning inside the barrel. If worried about pliers marks on your rod you can wrap another piece of leather around it too. I use a Delrin rod and the marks sand out easily. You will get some other answers. They all work but this is what works best for me.