Сделал скелет того, как примерно будет реализован сервис

app/api/v1/endpoints/youtube.py

@@ -0,0 +1,12 @@
+from fastapi import APIRouter
+from app.services import YouTubeService
+from app.schemas import DownloadResponse
+from app.schemas import DownloadRequest
+
+router = APIRouter()
+
+
+@router.post("/", response_model=DownloadResponse)
+async def download_video(data: DownloadRequest):
+    response_data = YouTubeService.download(data)
+    return response_data

app/api/v1/router.py

@@ -0,0 +1,8 @@
+from fastapi import APIRouter
+from app.api.v1.endpoints import youtube
+
+
+router = APIRouter()
+
+
+router.include_router(youtube.router, prefix="/youtube", tags=["YouTube"])