What do you mean by Pawpaw? The common name is used for a few different fruits. In the United States the common name of pawpaw is used most often in reference to Asimina trilobata or Asimina sps. In some semitropical regions the same name may be used for other fruits in the Annonaceae. In some regions however the name Pawpaw is utilized for Papaya (Carica papaya).
Why should you use any of these in the first place?
Plant extracts contain antimicrobials and this may be detrimental to the nodulating bacteria - you have to first test by in vitro antimicrobial assay - I am doubtful of neem at least.