Yes, there are countless companies producing and/or designing any kind of printed circuit boards. (Just an example from EU for a generalist is eurocircuits, but you can find many others)

Still the big question is what you really want to have.

If you have an own design or you are willing to pay for a completely new design, you can go to some generalist PCB company as I mentioned abowe.

With some small series with modifications for a well known design? You can go probably to the original producer company itself and ask for designing a variant for you. Other than the original company, might run into licensing issues.

Depending on how complicated your wish was you will get a cheap or expensive quotation.
You have to pay the project costs (design, tooling, coordination,...) and of course the variable costs (raw material, components, machine time,...)
Even the biggest brand companies (like samsung or similar) would do this for you, just probably not in the price range or minimal ammount, you would possibly prefer .