If I am correct in reading your question, some of the skin is not coming off the filet when you are slicing it off with your knife. If that is the case there are a few things you can do:
1. Make sure your fish are put on cold slush type ice immediately after they are caught. I also like to bleed all fish that I catch no matter what the species before I put them on ice. It keeps the flesh tighter and the skin easier to remove.
2. The angle of your filet knife while you are cutting is off by a little. Just applying a little more downward angle and pressure might help this. The knife needs to be sharp, too.
3. Having the right filet knife for the type of species you are filleting.
For example, when cleaning trout or mackerel, the more flexible the blade is, the easier it is to filet these species and get the skin off. For redfish, black drum, sheepshead etc., use a stiffer blade. Personally, I use a Cutco Fisherman's Solution Knife. It has an adjustable blade from about 7 inches to 10 inches, and holds its edge well. I have had it for about 10 years and use it on my Charter trips. It has a lifetime warranty and retails for quite a bit. I snapped mine a short time ag, but when I contacted Cutco, they mailed me a new one at no charge.
I also use a Mister Twister Saltwater electric knife. I use this on large scaled or tough-skinned fish like redfish, sheepshead, triggerfish, etc. The electric knife has a serrated edge and cuts through the toughest of fish. Note that it is full electric. I do not use a cordless. I had a cordless and it seemed to die out after a fish or two. I attached a photo of the Cutco Fisherman's Solution knife. Thank you for sending in your question to The Online Fisherman.
Here is a great video about properly filleting a fish. Really special thanks to Chef Mike Ward on YouTube. He does far more than fillet a fish now and then - it's only one of many great instructional guides he offers his subscribers. Some people are great in the kitchen. Some have a passion in their blood for great tastes and for imparting their wisdom on others. Chef Mike is one of those people.
Captain David M. Rieumont
The Online Fisherman Inc.
Captain David M Rieumont
You can check out Captain David himself from his incredible and very popular Patriotic Angler podcasts. They cover every bit of fishing you can imagine, and there are new ones being created constantly. David and his team remain one of best resources any fishing community has anywhere in the country.