Some routers have USB port for connecting storage device.I am searching for a (consumer/home) WiFi router which can download and seed torrent (directly to the storage device connected to the router via USB port) through router's UI or router management app(Android or ios app).i.e. Xiaomi mi router 3 can download torrent but cannot seed after completing download.Which router can also seed torrent after downloading.
You can get any of the routers which support the Tomato Open-source Router Firmware. This firmware includes in it the Transmission BitTorrent client which can do just about anything torrent...
I'd recommend specifically the AdvancedTomato breed of the Tomato firmware which improves a lot in the UI and looks of it.
Here is a list of routers it is available for https://advancedtomato.com/downloads, but if you want good performance take something - at least a bit - powerful. I think that the Netgear R7000 or the ASUS RT-AC66U or pretty good choice.
Asus RT-N66U Does have the same feature you are looking for.
I hope it will give you the same feeling as if you are downloading/uploading and seeding on your pc/laptop and moreover, it gives you more control over network.
following link contains more information about the router