Looking for a male to male ball valve that will connect to the fridge water line hose. The hose says it 1/4. I purchased a ball valve on the internet that was 1/4 male to male but was too big for the water line hose connection. Not sure how to purchase the correct size.
Refrigerator water/ice-maker lines are typically 1/4" tubing (poly or copper). The fittings usually found on these systems are 1/4" compression, which is designed to work with special compression nuts and ferrules which attach to the tubing and seal by squishing (compression) of the ferrule.
Your ball valve probably has 1/4" pipe thread (NPT) which is totally different but can be easily adapted to compression thread with a couple inexpensive adapters.
Note- it is common to also find hoses with braided stainless-steel jacket used for connection. These are also typically equipped with 1/4" compression thread, so they can be easily used on existing systems.