I spoke with Kevin Ramsey, Ohio Division of Wildlife, and he said that the fine on possession of a round goby really depends on the situation. For example, the penalty is going to be larger if you are caught selling them as bait. The maximum penalty for possession of a round goby is $250.00 and up to 30 days in jail.
There is good reasoning behind these regulations. Many of our introduced invasive species come from aquarium releases (i.e. goldfish). People have a habit of dumping un-wanted pets into natural bodies of water.
Invasive species are also released into our water bodies when fishermen dump their bait buckets over the side after they are done fishing. Let's say, for example, that some fishermen use a seine to net some minnows from Lake Erie. Some gobies also get caught in the net and go into the bait bucket. These fishermen decide that they don't want to fish on Lake Erie today, so they head to an inland lake. They fish all day. At the end of the day, there are still a few minnows left, so they just dump the bucket over the side of the boat, not realizing that there were round gobies in the bucket. These fishermen may have unknowingly introduced the round goby into a lake that didn't previously have them.
The Department of Natural Resources and other governing bodies, are worried that if people begin taking gobies and keeping them as pets or worse, using them as bait, round gobies will be spread to other un-contaminated water bodies.
As far as I know, it is not illegal to kill gobies. However, even if you kill them, you must throw them back. You cannot be caught in possession of either live or dead gobies.
Kelly Riesen, Fisheries Extension Program Coordinator, Ohio Sea Grant