What is reconcile of payment journal, when this process comes into picture and what is the navigation in AX to do this process?
It is checking the payment journal should be posted and it comes into normal business process for generating a payment run - look for the payment journal in AX.
also, suggest how to do a reconcile payment journal in ax after payment has posted
It depends upon the requirements because reconciliation happens as part of the payment process. If you mean bank reconciliation you will need to read the manual.