How to set FastAPI version to allow HTTP specifying version in accept header?

I am working on a project that requires to version FastAPI endpoints. We want to version the endpoint through HTTP accept header, for example:

headers={'Accept': 'application/json;version=1.0.1'}, 
headers={'Accept': 'application/json;version=1.0.2'}

Setting up the api version like this seem not work:

app = FastAPI(
        version=version,
        title="A title",
        description="Some description.",
    )

Does anyone know what else I need to do with this ?

Well maybe the version in path url could be better

sub apps docs

from fastapi import FastAPI

app = FastAPI()
v1 = FastAPI()

@v1.get("/app/")
def read_main():
    return {"message": "Hello World from api v1"}

v2 = FastAPI()

@v2.get("/app/")
def read_sub():
    return {"message": "Hello World from  api v2"}

app.mount("/api/v1", v1)
app.mount("/api/v2", v2)

You will see the auto docs for each app

localhost:8000/api/v1/docs

localhost:8000/api/v2/docs

But you always get the headers in request

from starlette.requests import Request

from fastapi import FastAPI
app = FastAPI()

@app.post("/hyper_mega_fast_service")
def fast_service(request: Request, ):

    aceept = request.headers.get('Accept')

    value = great_fuction_to_get_version_from_header(aceept)
    if value == '1.0.1': 
        "Do something"
        
    if value == '1.0.2': 
        "Do something"