My iphone 7 has no service for cellular service. I have updated the software but still no service. I recently replaced the battery but I don't hink it was genuine apple battery. Could this cause the loss of service.

Yes, it could be. Non Apple batteries can come from anywhere and usually they are cheap Chinese knockoffs that don't conform to Apple standards so they may not be able to provide the power required to run the phone properly

Also, see if this applies to you -

iPhone 7 Repair Program for "No Service" Issues - Apple Support

Either way, make an appointment at the Genius bar, they can diagnose the issue and provide an answer.

Do note however that they may not want to work on it as a non-authorized repair shop has opened your phone.

Genius Bar Reservation and Apple Support Options - Apple

Rather than the battery itself, even a minor mistake when changing the battery can damage the phone. For example, there are 2 screws that hold down the battery connector. They are different lengths, and switching them can short out the motherboard.

Pretty sure once the owner opens the phone and replaces anything, Apple is not going to touch the device or take it back for a service program.

Yup, that's why I mentioned it but it's still worth a try, sometimes you get a nice tech.