I keep hearing water turn on and off in the house... sounding like the toilet is flushing when in fact no one is flushing the toilet. It sounds like perhaps it is topping up the tank? The toilet is fairly new and I have no clue what to do to fix this. You can actually hear the water turn on and off and this happens about 3 times an hour. Thank you for any help you can give to me.

Go around and shut off the supply lines to your toilets, if it stops then you can start opening then one at a time to find which fill valve is bad. Adjust all fill valve floats so the water rises up and stops 1" below the top of the overflow tube.

It sounds like you have a bad flapper or the tank water level is too high.

Check the "critical level" Mark at least an inch over the top of the white overflow tube.

Check the tank water level, it should be at the mark in the tank 1" below the top of the over flow tube when the tank is filled and the ballcock shut down

Feel around the flapper flat edge. If it's wavy or you feel rough spots replace the flapper,
The linkage between the flapper and the flush lever should have 1/4" play when the tank is filled. Also, check the small tube coming out of the top of the ballcock and make sure it's connect to and draining into the white overflow tube.

Adjusting the level of water in the toilet tank keeps your toilet flushing completely. The water level normally falls about 1 inch below the rim of the overflow tube. Lower levels don't allow the float ball to raise high enough to close the ball cock; a water level that is too high will continuously run, wasting water and forcing you to listen to the running water all day.

Other ways to check if the flapper valve is leaking.
1. Shut off the angle valve to the toilet tank, check the water level it should be 1" below the top of the overflow tube and put a mark, after 1/2 hour check the level if it is below your mark this indication of the flapper valve leaking and needs to be replaced.
2. do the same shut off the angle valve and mark the water level, put some food coloring inside the tank and check after 1/2 hour if you see color in the bowl the flapper is leaking if your water level is high above the fill tube the color will so show in the bowl, Thanks, get back to s if the above would not help, Thanks.

John