The device you are looking for is called a femtocell. The problem is that to operate one you technically need a chunk of 4G licensed spectrum (which governments auction off for many hundreds millions of [insert currency of choice]).
You can buy femtocells normally from cellular operators for locations with bad reception and they sublease the spectrum to you as part of your cellular contract. They use your internet connection to forward connections to the operators network in order to allow access to the crypto keys needed to authenticate with the network and then to route data and calls into the operators network and on to the target. And even though you are providing the back haul for the femtocell the cellular provider still bills you as if you are using their normal network.
Another option is to use a SDR (Software Defined Radio), like a LimeSDR and one of the opensource projects (e.g. openBTS or Osmocom) to build your own, but again without the right license this would be illegal. The other problem with this is you might have to provide your own SIM cards that will bind you to your private network, getting hold of small numbers of custom SIM cards used to be very difficult as the suppliers would only sell them to recognised cellular providers. In these days of many MVNOs (Mobile Virtual Network Operators) it may be a little easier but it's been a long time since I checked.
Depending where you are in the world it may be possible to get a short term or very low power license. I know the Electromagnetic Fields festival in the UK got a license to run a GSM (2G) network for the duration of the festival in 2018. Details here.