I am assuming you aren't asking to become a PSP by yourself as that would require a lot more than just integration(you'll have to be listed under RBI to become a PSP, etc.)
But your problem can be solved by becoming a merchant which will use a PSP in the user's mobile phone.
Basically, you will create a URI and will send that as an intent. The PSP apps are given the guidelines to listen to the specific URI and hence, you can invoke the desired PSP app from the list(if you have many PSP apps installed).
The URI will contain the required information. The PSP app can get the details from the URI and the user can just confirm for the payment.
The response is being sent to the calling app with the transaction Id and some info. You can use that to carry on with your app's flow.
You can create the URI in the following way:
upi://pay?pa=icici/name&pn=USER_NAME&tid=422d97c1-f0fc-4bea-b24a-511ffa85e86f&am=442.87&tn=Test%transaction
and the intent can be created like:
Intent intent = new Intent();
intent.setData(Uri.parse(UPI));
Intent chooser = Intent.createChooser(intent, "Pay with...");
startActivityForResult(chooser, 1, null);
Listen to the PSP response in the onActivityResult method of your activity.
