Suggest for me a client adapter

I have 1 Ap and 1 repeater , The ipad and iphone can roam between these both Ap's.

I have like device that accept ethernet only , i want to link it with a Ap that can work in client mode (i want it to have the ability to roam between same SSID)

I bought many portable routers/ client adapter they did not roam in client mode. i didnt try dlink 1350
but i tried tenda , tplink , asus and many nothing works