So the basic problem is that I am setting up an Amazon connect instance and have successfully started recording calls too but I want the recording audio file to be stored in the S3 bucket in some format(.mp3, .mp4, etc) other than the default that is provided by Amazon (.wav).
Currently there is no capability to change audio format for Connect call recordings; it's fixed at 8 kHz, 16 bit WAV files. But you could set up a MediaConvert job to automatically convert to any format you'd like.
Alternatively you could have a trigger call a Lambda function to do the same thing. Here's a CloudFormation template that sets that up for you.
In both solutions, you might want to adjust the process a bit to delete the WAV file after conversion, to save on storage costs