in the market , in the market for: Is used when you want to buy something. For Example: If you have a car for sale, i am in the market. I am in the market for a beautiful car. on the market: Is used when something is available for buying or for sale. For example: My car is on the market.

I only know the first one.It means you are wishing to buy something.. for example "I am in the market for a second hand iphone.Do you have one?" means you wish to buy a second hand iphone. I don't think you can say the other two.They are incorrect.