I'm trying to make and app like Call Cheater(Originally developed for Symbian OS)
Is it possible to play a music during a phone conversation where receiver and caller should hear the same sound or music?
If yes how can I implement this?
You failed to find an app that does this because it is not possible.
The documentation clearly states (here):
Note: You can play back the audio data only to the standard output device. Currently, that is the mobile device speaker or a Bluetooth headset. You cannot play sound files in the conversation audio during a call.
The reason behind this decision has probably something to do with security: there are several scenarios where this capability could be used for cons.
(the OP is highly similar to this, hence I'm basically giving the same answer)