I have a 1968s penny in awesome condition and it weighs 3.2 grams. When you look around the edge you can see a seam where there is a sliver looking band. It also looks like a ridge around parts of edge on obverse. I attached the front and back of coin but trying to get a pic of the outside edge is proving hard.
This is unfortunately not an error of any kind. While in nice condition, a huge number of 1968-S cents are still surviving in Mint State. What you have is something that would grade roughly MS-65 RD, possibly worth 50 cents to the right collector.
The Obverse side of your copper Cent has a Misaligned die strike. That's a common issue. The weight difference is within mint tolerance. There's absolutely no silver in copper Planchet cents. But all in all it doesn't have any premium. You can keep any coin you want. No need to ask us
