I`ts battery fault or my phone`s?

So my battery lasts about half a day if I`m using it constantly, if not max one day. Bought on ebay battery, inserted phone overheated and battery drained 10% per min, bought another one showed me already 300+ charging cycle so it was same as my old battery, lasted couple of hours and was kinda hot too, when I insert my old battery phone is cool, but battery life is too short. Can I buy battery here? Is it any good? Or it`s maby iPhone fault? I discharged till it shuts down and its charging and powering on easily, no problems.